Solutions
Contents
Solutions#
Question 1#
1. Obtain the following tuples using therangecommand:
1. \((0, 1, 2, 3, 4, 5)\)
tuple(range(6))
(0, 1, 2, 3, 4, 5)
2. \((2, 3, 4, 5)\)
tuple(range(2, 6))
(2, 3, 4, 5)
3. \((2, 4, 6, 8)\)
tuple(range(2, 9, 2))
(2, 4, 6, 8)
4. \(-1, 2, 5, 8\)
tuple(range(-1, 9, 3))
(-1, 2, 5, 8)
Question 2#
2. By both generating and directly computing obtain the number of the following:
1. All permutations of \((0, 1, 2, 3, 4, 5)\).
Generating them all:
import itertools
digits = range(6)
permutations = tuple(itertools.permutations(digits))
permutations
((0, 1, 2, 3, 4, 5),
(0, 1, 2, 3, 5, 4),
(0, 1, 2, 4, 3, 5),
(0, 1, 2, 4, 5, 3),
(0, 1, 2, 5, 3, 4),
(0, 1, 2, 5, 4, 3),
(0, 1, 3, 2, 4, 5),
(0, 1, 3, 2, 5, 4),
(0, 1, 3, 4, 2, 5),
(0, 1, 3, 4, 5, 2),
(0, 1, 3, 5, 2, 4),
(0, 1, 3, 5, 4, 2),
(0, 1, 4, 2, 3, 5),
(0, 1, 4, 2, 5, 3),
(0, 1, 4, 3, 2, 5),
(0, 1, 4, 3, 5, 2),
(0, 1, 4, 5, 2, 3),
(0, 1, 4, 5, 3, 2),
(0, 1, 5, 2, 3, 4),
(0, 1, 5, 2, 4, 3),
(0, 1, 5, 3, 2, 4),
(0, 1, 5, 3, 4, 2),
(0, 1, 5, 4, 2, 3),
(0, 1, 5, 4, 3, 2),
(0, 2, 1, 3, 4, 5),
(0, 2, 1, 3, 5, 4),
(0, 2, 1, 4, 3, 5),
(0, 2, 1, 4, 5, 3),
(0, 2, 1, 5, 3, 4),
(0, 2, 1, 5, 4, 3),
(0, 2, 3, 1, 4, 5),
(0, 2, 3, 1, 5, 4),
(0, 2, 3, 4, 1, 5),
(0, 2, 3, 4, 5, 1),
(0, 2, 3, 5, 1, 4),
(0, 2, 3, 5, 4, 1),
(0, 2, 4, 1, 3, 5),
(0, 2, 4, 1, 5, 3),
(0, 2, 4, 3, 1, 5),
(0, 2, 4, 3, 5, 1),
(0, 2, 4, 5, 1, 3),
(0, 2, 4, 5, 3, 1),
(0, 2, 5, 1, 3, 4),
(0, 2, 5, 1, 4, 3),
(0, 2, 5, 3, 1, 4),
(0, 2, 5, 3, 4, 1),
(0, 2, 5, 4, 1, 3),
(0, 2, 5, 4, 3, 1),
(0, 3, 1, 2, 4, 5),
(0, 3, 1, 2, 5, 4),
(0, 3, 1, 4, 2, 5),
(0, 3, 1, 4, 5, 2),
(0, 3, 1, 5, 2, 4),
(0, 3, 1, 5, 4, 2),
(0, 3, 2, 1, 4, 5),
(0, 3, 2, 1, 5, 4),
(0, 3, 2, 4, 1, 5),
(0, 3, 2, 4, 5, 1),
(0, 3, 2, 5, 1, 4),
(0, 3, 2, 5, 4, 1),
(0, 3, 4, 1, 2, 5),
(0, 3, 4, 1, 5, 2),
(0, 3, 4, 2, 1, 5),
(0, 3, 4, 2, 5, 1),
(0, 3, 4, 5, 1, 2),
(0, 3, 4, 5, 2, 1),
(0, 3, 5, 1, 2, 4),
(0, 3, 5, 1, 4, 2),
(0, 3, 5, 2, 1, 4),
(0, 3, 5, 2, 4, 1),
(0, 3, 5, 4, 1, 2),
(0, 3, 5, 4, 2, 1),
(0, 4, 1, 2, 3, 5),
(0, 4, 1, 2, 5, 3),
(0, 4, 1, 3, 2, 5),
(0, 4, 1, 3, 5, 2),
(0, 4, 1, 5, 2, 3),
(0, 4, 1, 5, 3, 2),
(0, 4, 2, 1, 3, 5),
(0, 4, 2, 1, 5, 3),
(0, 4, 2, 3, 1, 5),
(0, 4, 2, 3, 5, 1),
(0, 4, 2, 5, 1, 3),
(0, 4, 2, 5, 3, 1),
(0, 4, 3, 1, 2, 5),
(0, 4, 3, 1, 5, 2),
(0, 4, 3, 2, 1, 5),
(0, 4, 3, 2, 5, 1),
(0, 4, 3, 5, 1, 2),
(0, 4, 3, 5, 2, 1),
(0, 4, 5, 1, 2, 3),
(0, 4, 5, 1, 3, 2),
(0, 4, 5, 2, 1, 3),
(0, 4, 5, 2, 3, 1),
(0, 4, 5, 3, 1, 2),
(0, 4, 5, 3, 2, 1),
(0, 5, 1, 2, 3, 4),
(0, 5, 1, 2, 4, 3),
(0, 5, 1, 3, 2, 4),
(0, 5, 1, 3, 4, 2),
(0, 5, 1, 4, 2, 3),
(0, 5, 1, 4, 3, 2),
(0, 5, 2, 1, 3, 4),
(0, 5, 2, 1, 4, 3),
(0, 5, 2, 3, 1, 4),
(0, 5, 2, 3, 4, 1),
(0, 5, 2, 4, 1, 3),
(0, 5, 2, 4, 3, 1),
(0, 5, 3, 1, 2, 4),
(0, 5, 3, 1, 4, 2),
(0, 5, 3, 2, 1, 4),
(0, 5, 3, 2, 4, 1),
(0, 5, 3, 4, 1, 2),
(0, 5, 3, 4, 2, 1),
(0, 5, 4, 1, 2, 3),
(0, 5, 4, 1, 3, 2),
(0, 5, 4, 2, 1, 3),
(0, 5, 4, 2, 3, 1),
(0, 5, 4, 3, 1, 2),
(0, 5, 4, 3, 2, 1),
(1, 0, 2, 3, 4, 5),
(1, 0, 2, 3, 5, 4),
(1, 0, 2, 4, 3, 5),
(1, 0, 2, 4, 5, 3),
(1, 0, 2, 5, 3, 4),
(1, 0, 2, 5, 4, 3),
(1, 0, 3, 2, 4, 5),
(1, 0, 3, 2, 5, 4),
(1, 0, 3, 4, 2, 5),
(1, 0, 3, 4, 5, 2),
(1, 0, 3, 5, 2, 4),
(1, 0, 3, 5, 4, 2),
(1, 0, 4, 2, 3, 5),
(1, 0, 4, 2, 5, 3),
(1, 0, 4, 3, 2, 5),
(1, 0, 4, 3, 5, 2),
(1, 0, 4, 5, 2, 3),
(1, 0, 4, 5, 3, 2),
(1, 0, 5, 2, 3, 4),
(1, 0, 5, 2, 4, 3),
(1, 0, 5, 3, 2, 4),
(1, 0, 5, 3, 4, 2),
(1, 0, 5, 4, 2, 3),
(1, 0, 5, 4, 3, 2),
(1, 2, 0, 3, 4, 5),
(1, 2, 0, 3, 5, 4),
(1, 2, 0, 4, 3, 5),
(1, 2, 0, 4, 5, 3),
(1, 2, 0, 5, 3, 4),
(1, 2, 0, 5, 4, 3),
(1, 2, 3, 0, 4, 5),
(1, 2, 3, 0, 5, 4),
(1, 2, 3, 4, 0, 5),
(1, 2, 3, 4, 5, 0),
(1, 2, 3, 5, 0, 4),
(1, 2, 3, 5, 4, 0),
(1, 2, 4, 0, 3, 5),
(1, 2, 4, 0, 5, 3),
(1, 2, 4, 3, 0, 5),
(1, 2, 4, 3, 5, 0),
(1, 2, 4, 5, 0, 3),
(1, 2, 4, 5, 3, 0),
(1, 2, 5, 0, 3, 4),
(1, 2, 5, 0, 4, 3),
(1, 2, 5, 3, 0, 4),
(1, 2, 5, 3, 4, 0),
(1, 2, 5, 4, 0, 3),
(1, 2, 5, 4, 3, 0),
(1, 3, 0, 2, 4, 5),
(1, 3, 0, 2, 5, 4),
(1, 3, 0, 4, 2, 5),
(1, 3, 0, 4, 5, 2),
(1, 3, 0, 5, 2, 4),
(1, 3, 0, 5, 4, 2),
(1, 3, 2, 0, 4, 5),
(1, 3, 2, 0, 5, 4),
(1, 3, 2, 4, 0, 5),
(1, 3, 2, 4, 5, 0),
(1, 3, 2, 5, 0, 4),
(1, 3, 2, 5, 4, 0),
(1, 3, 4, 0, 2, 5),
(1, 3, 4, 0, 5, 2),
(1, 3, 4, 2, 0, 5),
(1, 3, 4, 2, 5, 0),
(1, 3, 4, 5, 0, 2),
(1, 3, 4, 5, 2, 0),
(1, 3, 5, 0, 2, 4),
(1, 3, 5, 0, 4, 2),
(1, 3, 5, 2, 0, 4),
(1, 3, 5, 2, 4, 0),
(1, 3, 5, 4, 0, 2),
(1, 3, 5, 4, 2, 0),
(1, 4, 0, 2, 3, 5),
(1, 4, 0, 2, 5, 3),
(1, 4, 0, 3, 2, 5),
(1, 4, 0, 3, 5, 2),
(1, 4, 0, 5, 2, 3),
(1, 4, 0, 5, 3, 2),
(1, 4, 2, 0, 3, 5),
(1, 4, 2, 0, 5, 3),
(1, 4, 2, 3, 0, 5),
(1, 4, 2, 3, 5, 0),
(1, 4, 2, 5, 0, 3),
(1, 4, 2, 5, 3, 0),
(1, 4, 3, 0, 2, 5),
(1, 4, 3, 0, 5, 2),
(1, 4, 3, 2, 0, 5),
(1, 4, 3, 2, 5, 0),
(1, 4, 3, 5, 0, 2),
(1, 4, 3, 5, 2, 0),
(1, 4, 5, 0, 2, 3),
(1, 4, 5, 0, 3, 2),
(1, 4, 5, 2, 0, 3),
(1, 4, 5, 2, 3, 0),
(1, 4, 5, 3, 0, 2),
(1, 4, 5, 3, 2, 0),
(1, 5, 0, 2, 3, 4),
(1, 5, 0, 2, 4, 3),
(1, 5, 0, 3, 2, 4),
(1, 5, 0, 3, 4, 2),
(1, 5, 0, 4, 2, 3),
(1, 5, 0, 4, 3, 2),
(1, 5, 2, 0, 3, 4),
(1, 5, 2, 0, 4, 3),
(1, 5, 2, 3, 0, 4),
(1, 5, 2, 3, 4, 0),
(1, 5, 2, 4, 0, 3),
(1, 5, 2, 4, 3, 0),
(1, 5, 3, 0, 2, 4),
(1, 5, 3, 0, 4, 2),
(1, 5, 3, 2, 0, 4),
(1, 5, 3, 2, 4, 0),
(1, 5, 3, 4, 0, 2),
(1, 5, 3, 4, 2, 0),
(1, 5, 4, 0, 2, 3),
(1, 5, 4, 0, 3, 2),
(1, 5, 4, 2, 0, 3),
(1, 5, 4, 2, 3, 0),
(1, 5, 4, 3, 0, 2),
(1, 5, 4, 3, 2, 0),
(2, 0, 1, 3, 4, 5),
(2, 0, 1, 3, 5, 4),
(2, 0, 1, 4, 3, 5),
(2, 0, 1, 4, 5, 3),
(2, 0, 1, 5, 3, 4),
(2, 0, 1, 5, 4, 3),
(2, 0, 3, 1, 4, 5),
(2, 0, 3, 1, 5, 4),
(2, 0, 3, 4, 1, 5),
(2, 0, 3, 4, 5, 1),
(2, 0, 3, 5, 1, 4),
(2, 0, 3, 5, 4, 1),
(2, 0, 4, 1, 3, 5),
(2, 0, 4, 1, 5, 3),
(2, 0, 4, 3, 1, 5),
(2, 0, 4, 3, 5, 1),
(2, 0, 4, 5, 1, 3),
(2, 0, 4, 5, 3, 1),
(2, 0, 5, 1, 3, 4),
(2, 0, 5, 1, 4, 3),
(2, 0, 5, 3, 1, 4),
(2, 0, 5, 3, 4, 1),
(2, 0, 5, 4, 1, 3),
(2, 0, 5, 4, 3, 1),
(2, 1, 0, 3, 4, 5),
(2, 1, 0, 3, 5, 4),
(2, 1, 0, 4, 3, 5),
(2, 1, 0, 4, 5, 3),
(2, 1, 0, 5, 3, 4),
(2, 1, 0, 5, 4, 3),
(2, 1, 3, 0, 4, 5),
(2, 1, 3, 0, 5, 4),
(2, 1, 3, 4, 0, 5),
(2, 1, 3, 4, 5, 0),
(2, 1, 3, 5, 0, 4),
(2, 1, 3, 5, 4, 0),
(2, 1, 4, 0, 3, 5),
(2, 1, 4, 0, 5, 3),
(2, 1, 4, 3, 0, 5),
(2, 1, 4, 3, 5, 0),
(2, 1, 4, 5, 0, 3),
(2, 1, 4, 5, 3, 0),
(2, 1, 5, 0, 3, 4),
(2, 1, 5, 0, 4, 3),
(2, 1, 5, 3, 0, 4),
(2, 1, 5, 3, 4, 0),
(2, 1, 5, 4, 0, 3),
(2, 1, 5, 4, 3, 0),
(2, 3, 0, 1, 4, 5),
(2, 3, 0, 1, 5, 4),
(2, 3, 0, 4, 1, 5),
(2, 3, 0, 4, 5, 1),
(2, 3, 0, 5, 1, 4),
(2, 3, 0, 5, 4, 1),
(2, 3, 1, 0, 4, 5),
(2, 3, 1, 0, 5, 4),
(2, 3, 1, 4, 0, 5),
(2, 3, 1, 4, 5, 0),
(2, 3, 1, 5, 0, 4),
(2, 3, 1, 5, 4, 0),
(2, 3, 4, 0, 1, 5),
(2, 3, 4, 0, 5, 1),
(2, 3, 4, 1, 0, 5),
(2, 3, 4, 1, 5, 0),
(2, 3, 4, 5, 0, 1),
(2, 3, 4, 5, 1, 0),
(2, 3, 5, 0, 1, 4),
(2, 3, 5, 0, 4, 1),
(2, 3, 5, 1, 0, 4),
(2, 3, 5, 1, 4, 0),
(2, 3, 5, 4, 0, 1),
(2, 3, 5, 4, 1, 0),
(2, 4, 0, 1, 3, 5),
(2, 4, 0, 1, 5, 3),
(2, 4, 0, 3, 1, 5),
(2, 4, 0, 3, 5, 1),
(2, 4, 0, 5, 1, 3),
(2, 4, 0, 5, 3, 1),
(2, 4, 1, 0, 3, 5),
(2, 4, 1, 0, 5, 3),
(2, 4, 1, 3, 0, 5),
(2, 4, 1, 3, 5, 0),
(2, 4, 1, 5, 0, 3),
(2, 4, 1, 5, 3, 0),
(2, 4, 3, 0, 1, 5),
(2, 4, 3, 0, 5, 1),
(2, 4, 3, 1, 0, 5),
(2, 4, 3, 1, 5, 0),
(2, 4, 3, 5, 0, 1),
(2, 4, 3, 5, 1, 0),
(2, 4, 5, 0, 1, 3),
(2, 4, 5, 0, 3, 1),
(2, 4, 5, 1, 0, 3),
(2, 4, 5, 1, 3, 0),
(2, 4, 5, 3, 0, 1),
(2, 4, 5, 3, 1, 0),
(2, 5, 0, 1, 3, 4),
(2, 5, 0, 1, 4, 3),
(2, 5, 0, 3, 1, 4),
(2, 5, 0, 3, 4, 1),
(2, 5, 0, 4, 1, 3),
(2, 5, 0, 4, 3, 1),
(2, 5, 1, 0, 3, 4),
(2, 5, 1, 0, 4, 3),
(2, 5, 1, 3, 0, 4),
(2, 5, 1, 3, 4, 0),
(2, 5, 1, 4, 0, 3),
(2, 5, 1, 4, 3, 0),
(2, 5, 3, 0, 1, 4),
(2, 5, 3, 0, 4, 1),
(2, 5, 3, 1, 0, 4),
(2, 5, 3, 1, 4, 0),
(2, 5, 3, 4, 0, 1),
(2, 5, 3, 4, 1, 0),
(2, 5, 4, 0, 1, 3),
(2, 5, 4, 0, 3, 1),
(2, 5, 4, 1, 0, 3),
(2, 5, 4, 1, 3, 0),
(2, 5, 4, 3, 0, 1),
(2, 5, 4, 3, 1, 0),
(3, 0, 1, 2, 4, 5),
(3, 0, 1, 2, 5, 4),
(3, 0, 1, 4, 2, 5),
(3, 0, 1, 4, 5, 2),
(3, 0, 1, 5, 2, 4),
(3, 0, 1, 5, 4, 2),
(3, 0, 2, 1, 4, 5),
(3, 0, 2, 1, 5, 4),
(3, 0, 2, 4, 1, 5),
(3, 0, 2, 4, 5, 1),
(3, 0, 2, 5, 1, 4),
(3, 0, 2, 5, 4, 1),
(3, 0, 4, 1, 2, 5),
(3, 0, 4, 1, 5, 2),
(3, 0, 4, 2, 1, 5),
(3, 0, 4, 2, 5, 1),
(3, 0, 4, 5, 1, 2),
(3, 0, 4, 5, 2, 1),
(3, 0, 5, 1, 2, 4),
(3, 0, 5, 1, 4, 2),
(3, 0, 5, 2, 1, 4),
(3, 0, 5, 2, 4, 1),
(3, 0, 5, 4, 1, 2),
(3, 0, 5, 4, 2, 1),
(3, 1, 0, 2, 4, 5),
(3, 1, 0, 2, 5, 4),
(3, 1, 0, 4, 2, 5),
(3, 1, 0, 4, 5, 2),
(3, 1, 0, 5, 2, 4),
(3, 1, 0, 5, 4, 2),
(3, 1, 2, 0, 4, 5),
(3, 1, 2, 0, 5, 4),
(3, 1, 2, 4, 0, 5),
(3, 1, 2, 4, 5, 0),
(3, 1, 2, 5, 0, 4),
(3, 1, 2, 5, 4, 0),
(3, 1, 4, 0, 2, 5),
(3, 1, 4, 0, 5, 2),
(3, 1, 4, 2, 0, 5),
(3, 1, 4, 2, 5, 0),
(3, 1, 4, 5, 0, 2),
(3, 1, 4, 5, 2, 0),
(3, 1, 5, 0, 2, 4),
(3, 1, 5, 0, 4, 2),
(3, 1, 5, 2, 0, 4),
(3, 1, 5, 2, 4, 0),
(3, 1, 5, 4, 0, 2),
(3, 1, 5, 4, 2, 0),
(3, 2, 0, 1, 4, 5),
(3, 2, 0, 1, 5, 4),
(3, 2, 0, 4, 1, 5),
(3, 2, 0, 4, 5, 1),
(3, 2, 0, 5, 1, 4),
(3, 2, 0, 5, 4, 1),
(3, 2, 1, 0, 4, 5),
(3, 2, 1, 0, 5, 4),
(3, 2, 1, 4, 0, 5),
(3, 2, 1, 4, 5, 0),
(3, 2, 1, 5, 0, 4),
(3, 2, 1, 5, 4, 0),
(3, 2, 4, 0, 1, 5),
(3, 2, 4, 0, 5, 1),
(3, 2, 4, 1, 0, 5),
(3, 2, 4, 1, 5, 0),
(3, 2, 4, 5, 0, 1),
(3, 2, 4, 5, 1, 0),
(3, 2, 5, 0, 1, 4),
(3, 2, 5, 0, 4, 1),
(3, 2, 5, 1, 0, 4),
(3, 2, 5, 1, 4, 0),
(3, 2, 5, 4, 0, 1),
(3, 2, 5, 4, 1, 0),
(3, 4, 0, 1, 2, 5),
(3, 4, 0, 1, 5, 2),
(3, 4, 0, 2, 1, 5),
(3, 4, 0, 2, 5, 1),
(3, 4, 0, 5, 1, 2),
(3, 4, 0, 5, 2, 1),
(3, 4, 1, 0, 2, 5),
(3, 4, 1, 0, 5, 2),
(3, 4, 1, 2, 0, 5),
(3, 4, 1, 2, 5, 0),
(3, 4, 1, 5, 0, 2),
(3, 4, 1, 5, 2, 0),
(3, 4, 2, 0, 1, 5),
(3, 4, 2, 0, 5, 1),
(3, 4, 2, 1, 0, 5),
(3, 4, 2, 1, 5, 0),
(3, 4, 2, 5, 0, 1),
(3, 4, 2, 5, 1, 0),
(3, 4, 5, 0, 1, 2),
(3, 4, 5, 0, 2, 1),
(3, 4, 5, 1, 0, 2),
(3, 4, 5, 1, 2, 0),
(3, 4, 5, 2, 0, 1),
(3, 4, 5, 2, 1, 0),
(3, 5, 0, 1, 2, 4),
(3, 5, 0, 1, 4, 2),
(3, 5, 0, 2, 1, 4),
(3, 5, 0, 2, 4, 1),
(3, 5, 0, 4, 1, 2),
(3, 5, 0, 4, 2, 1),
(3, 5, 1, 0, 2, 4),
(3, 5, 1, 0, 4, 2),
(3, 5, 1, 2, 0, 4),
(3, 5, 1, 2, 4, 0),
(3, 5, 1, 4, 0, 2),
(3, 5, 1, 4, 2, 0),
(3, 5, 2, 0, 1, 4),
(3, 5, 2, 0, 4, 1),
(3, 5, 2, 1, 0, 4),
(3, 5, 2, 1, 4, 0),
(3, 5, 2, 4, 0, 1),
(3, 5, 2, 4, 1, 0),
(3, 5, 4, 0, 1, 2),
(3, 5, 4, 0, 2, 1),
(3, 5, 4, 1, 0, 2),
(3, 5, 4, 1, 2, 0),
(3, 5, 4, 2, 0, 1),
(3, 5, 4, 2, 1, 0),
(4, 0, 1, 2, 3, 5),
(4, 0, 1, 2, 5, 3),
(4, 0, 1, 3, 2, 5),
(4, 0, 1, 3, 5, 2),
(4, 0, 1, 5, 2, 3),
(4, 0, 1, 5, 3, 2),
(4, 0, 2, 1, 3, 5),
(4, 0, 2, 1, 5, 3),
(4, 0, 2, 3, 1, 5),
(4, 0, 2, 3, 5, 1),
(4, 0, 2, 5, 1, 3),
(4, 0, 2, 5, 3, 1),
(4, 0, 3, 1, 2, 5),
(4, 0, 3, 1, 5, 2),
(4, 0, 3, 2, 1, 5),
(4, 0, 3, 2, 5, 1),
(4, 0, 3, 5, 1, 2),
(4, 0, 3, 5, 2, 1),
(4, 0, 5, 1, 2, 3),
(4, 0, 5, 1, 3, 2),
(4, 0, 5, 2, 1, 3),
(4, 0, 5, 2, 3, 1),
(4, 0, 5, 3, 1, 2),
(4, 0, 5, 3, 2, 1),
(4, 1, 0, 2, 3, 5),
(4, 1, 0, 2, 5, 3),
(4, 1, 0, 3, 2, 5),
(4, 1, 0, 3, 5, 2),
(4, 1, 0, 5, 2, 3),
(4, 1, 0, 5, 3, 2),
(4, 1, 2, 0, 3, 5),
(4, 1, 2, 0, 5, 3),
(4, 1, 2, 3, 0, 5),
(4, 1, 2, 3, 5, 0),
(4, 1, 2, 5, 0, 3),
(4, 1, 2, 5, 3, 0),
(4, 1, 3, 0, 2, 5),
(4, 1, 3, 0, 5, 2),
(4, 1, 3, 2, 0, 5),
(4, 1, 3, 2, 5, 0),
(4, 1, 3, 5, 0, 2),
(4, 1, 3, 5, 2, 0),
(4, 1, 5, 0, 2, 3),
(4, 1, 5, 0, 3, 2),
(4, 1, 5, 2, 0, 3),
(4, 1, 5, 2, 3, 0),
(4, 1, 5, 3, 0, 2),
(4, 1, 5, 3, 2, 0),
(4, 2, 0, 1, 3, 5),
(4, 2, 0, 1, 5, 3),
(4, 2, 0, 3, 1, 5),
(4, 2, 0, 3, 5, 1),
(4, 2, 0, 5, 1, 3),
(4, 2, 0, 5, 3, 1),
(4, 2, 1, 0, 3, 5),
(4, 2, 1, 0, 5, 3),
(4, 2, 1, 3, 0, 5),
(4, 2, 1, 3, 5, 0),
(4, 2, 1, 5, 0, 3),
(4, 2, 1, 5, 3, 0),
(4, 2, 3, 0, 1, 5),
(4, 2, 3, 0, 5, 1),
(4, 2, 3, 1, 0, 5),
(4, 2, 3, 1, 5, 0),
(4, 2, 3, 5, 0, 1),
(4, 2, 3, 5, 1, 0),
(4, 2, 5, 0, 1, 3),
(4, 2, 5, 0, 3, 1),
(4, 2, 5, 1, 0, 3),
(4, 2, 5, 1, 3, 0),
(4, 2, 5, 3, 0, 1),
(4, 2, 5, 3, 1, 0),
(4, 3, 0, 1, 2, 5),
(4, 3, 0, 1, 5, 2),
(4, 3, 0, 2, 1, 5),
(4, 3, 0, 2, 5, 1),
(4, 3, 0, 5, 1, 2),
(4, 3, 0, 5, 2, 1),
(4, 3, 1, 0, 2, 5),
(4, 3, 1, 0, 5, 2),
(4, 3, 1, 2, 0, 5),
(4, 3, 1, 2, 5, 0),
(4, 3, 1, 5, 0, 2),
(4, 3, 1, 5, 2, 0),
(4, 3, 2, 0, 1, 5),
(4, 3, 2, 0, 5, 1),
(4, 3, 2, 1, 0, 5),
(4, 3, 2, 1, 5, 0),
(4, 3, 2, 5, 0, 1),
(4, 3, 2, 5, 1, 0),
(4, 3, 5, 0, 1, 2),
(4, 3, 5, 0, 2, 1),
(4, 3, 5, 1, 0, 2),
(4, 3, 5, 1, 2, 0),
(4, 3, 5, 2, 0, 1),
(4, 3, 5, 2, 1, 0),
(4, 5, 0, 1, 2, 3),
(4, 5, 0, 1, 3, 2),
(4, 5, 0, 2, 1, 3),
(4, 5, 0, 2, 3, 1),
(4, 5, 0, 3, 1, 2),
(4, 5, 0, 3, 2, 1),
(4, 5, 1, 0, 2, 3),
(4, 5, 1, 0, 3, 2),
(4, 5, 1, 2, 0, 3),
(4, 5, 1, 2, 3, 0),
(4, 5, 1, 3, 0, 2),
(4, 5, 1, 3, 2, 0),
(4, 5, 2, 0, 1, 3),
(4, 5, 2, 0, 3, 1),
(4, 5, 2, 1, 0, 3),
(4, 5, 2, 1, 3, 0),
(4, 5, 2, 3, 0, 1),
(4, 5, 2, 3, 1, 0),
(4, 5, 3, 0, 1, 2),
(4, 5, 3, 0, 2, 1),
(4, 5, 3, 1, 0, 2),
(4, 5, 3, 1, 2, 0),
(4, 5, 3, 2, 0, 1),
(4, 5, 3, 2, 1, 0),
(5, 0, 1, 2, 3, 4),
(5, 0, 1, 2, 4, 3),
(5, 0, 1, 3, 2, 4),
(5, 0, 1, 3, 4, 2),
(5, 0, 1, 4, 2, 3),
(5, 0, 1, 4, 3, 2),
(5, 0, 2, 1, 3, 4),
(5, 0, 2, 1, 4, 3),
(5, 0, 2, 3, 1, 4),
(5, 0, 2, 3, 4, 1),
(5, 0, 2, 4, 1, 3),
(5, 0, 2, 4, 3, 1),
(5, 0, 3, 1, 2, 4),
(5, 0, 3, 1, 4, 2),
(5, 0, 3, 2, 1, 4),
(5, 0, 3, 2, 4, 1),
(5, 0, 3, 4, 1, 2),
(5, 0, 3, 4, 2, 1),
(5, 0, 4, 1, 2, 3),
(5, 0, 4, 1, 3, 2),
(5, 0, 4, 2, 1, 3),
(5, 0, 4, 2, 3, 1),
(5, 0, 4, 3, 1, 2),
(5, 0, 4, 3, 2, 1),
(5, 1, 0, 2, 3, 4),
(5, 1, 0, 2, 4, 3),
(5, 1, 0, 3, 2, 4),
(5, 1, 0, 3, 4, 2),
(5, 1, 0, 4, 2, 3),
(5, 1, 0, 4, 3, 2),
(5, 1, 2, 0, 3, 4),
(5, 1, 2, 0, 4, 3),
(5, 1, 2, 3, 0, 4),
(5, 1, 2, 3, 4, 0),
(5, 1, 2, 4, 0, 3),
(5, 1, 2, 4, 3, 0),
(5, 1, 3, 0, 2, 4),
(5, 1, 3, 0, 4, 2),
(5, 1, 3, 2, 0, 4),
(5, 1, 3, 2, 4, 0),
(5, 1, 3, 4, 0, 2),
(5, 1, 3, 4, 2, 0),
(5, 1, 4, 0, 2, 3),
(5, 1, 4, 0, 3, 2),
(5, 1, 4, 2, 0, 3),
(5, 1, 4, 2, 3, 0),
(5, 1, 4, 3, 0, 2),
(5, 1, 4, 3, 2, 0),
(5, 2, 0, 1, 3, 4),
(5, 2, 0, 1, 4, 3),
(5, 2, 0, 3, 1, 4),
(5, 2, 0, 3, 4, 1),
(5, 2, 0, 4, 1, 3),
(5, 2, 0, 4, 3, 1),
(5, 2, 1, 0, 3, 4),
(5, 2, 1, 0, 4, 3),
(5, 2, 1, 3, 0, 4),
(5, 2, 1, 3, 4, 0),
(5, 2, 1, 4, 0, 3),
(5, 2, 1, 4, 3, 0),
(5, 2, 3, 0, 1, 4),
(5, 2, 3, 0, 4, 1),
(5, 2, 3, 1, 0, 4),
(5, 2, 3, 1, 4, 0),
(5, 2, 3, 4, 0, 1),
(5, 2, 3, 4, 1, 0),
(5, 2, 4, 0, 1, 3),
(5, 2, 4, 0, 3, 1),
(5, 2, 4, 1, 0, 3),
(5, 2, 4, 1, 3, 0),
(5, 2, 4, 3, 0, 1),
(5, 2, 4, 3, 1, 0),
(5, 3, 0, 1, 2, 4),
(5, 3, 0, 1, 4, 2),
(5, 3, 0, 2, 1, 4),
(5, 3, 0, 2, 4, 1),
(5, 3, 0, 4, 1, 2),
(5, 3, 0, 4, 2, 1),
(5, 3, 1, 0, 2, 4),
(5, 3, 1, 0, 4, 2),
(5, 3, 1, 2, 0, 4),
(5, 3, 1, 2, 4, 0),
(5, 3, 1, 4, 0, 2),
(5, 3, 1, 4, 2, 0),
(5, 3, 2, 0, 1, 4),
(5, 3, 2, 0, 4, 1),
(5, 3, 2, 1, 0, 4),
(5, 3, 2, 1, 4, 0),
(5, 3, 2, 4, 0, 1),
(5, 3, 2, 4, 1, 0),
(5, 3, 4, 0, 1, 2),
(5, 3, 4, 0, 2, 1),
(5, 3, 4, 1, 0, 2),
(5, 3, 4, 1, 2, 0),
(5, 3, 4, 2, 0, 1),
(5, 3, 4, 2, 1, 0),
(5, 4, 0, 1, 2, 3),
(5, 4, 0, 1, 3, 2),
(5, 4, 0, 2, 1, 3),
(5, 4, 0, 2, 3, 1),
(5, 4, 0, 3, 1, 2),
(5, 4, 0, 3, 2, 1),
(5, 4, 1, 0, 2, 3),
(5, 4, 1, 0, 3, 2),
(5, 4, 1, 2, 0, 3),
(5, 4, 1, 2, 3, 0),
(5, 4, 1, 3, 0, 2),
(5, 4, 1, 3, 2, 0),
(5, 4, 2, 0, 1, 3),
(5, 4, 2, 0, 3, 1),
(5, 4, 2, 1, 0, 3),
(5, 4, 2, 1, 3, 0),
(5, 4, 2, 3, 0, 1),
(5, 4, 2, 3, 1, 0),
(5, 4, 3, 0, 1, 2),
(5, 4, 3, 0, 2, 1),
(5, 4, 3, 1, 0, 2),
(5, 4, 3, 1, 2, 0),
(5, 4, 3, 2, 0, 1),
(5, 4, 3, 2, 1, 0))
Counting them:
len(permutations)
720
Computing the number directly:
import math
math.factorial(6)
720
2. All permutations of \((A, B, C)\).
Generating them all:
letters = ("A", "B", "C")
permutations = tuple(itertools.permutations(letters))
permutations
(('A', 'B', 'C'),
('A', 'C', 'B'),
('B', 'A', 'C'),
('B', 'C', 'A'),
('C', 'A', 'B'),
('C', 'B', 'A'))
Counting them:
len(permutations)
6
Computing the number directly:
math.factorial(3)
6
3. Permutations of size 3 of \((0, 1, 2, 3, 4, 5)\).
Generating them all:
digits = range(6)
permutations = tuple(itertools.permutations(digits, r=3))
permutations
((0, 1, 2),
(0, 1, 3),
(0, 1, 4),
(0, 1, 5),
(0, 2, 1),
(0, 2, 3),
(0, 2, 4),
(0, 2, 5),
(0, 3, 1),
(0, 3, 2),
(0, 3, 4),
(0, 3, 5),
(0, 4, 1),
(0, 4, 2),
(0, 4, 3),
(0, 4, 5),
(0, 5, 1),
(0, 5, 2),
(0, 5, 3),
(0, 5, 4),
(1, 0, 2),
(1, 0, 3),
(1, 0, 4),
(1, 0, 5),
(1, 2, 0),
(1, 2, 3),
(1, 2, 4),
(1, 2, 5),
(1, 3, 0),
(1, 3, 2),
(1, 3, 4),
(1, 3, 5),
(1, 4, 0),
(1, 4, 2),
(1, 4, 3),
(1, 4, 5),
(1, 5, 0),
(1, 5, 2),
(1, 5, 3),
(1, 5, 4),
(2, 0, 1),
(2, 0, 3),
(2, 0, 4),
(2, 0, 5),
(2, 1, 0),
(2, 1, 3),
(2, 1, 4),
(2, 1, 5),
(2, 3, 0),
(2, 3, 1),
(2, 3, 4),
(2, 3, 5),
(2, 4, 0),
(2, 4, 1),
(2, 4, 3),
(2, 4, 5),
(2, 5, 0),
(2, 5, 1),
(2, 5, 3),
(2, 5, 4),
(3, 0, 1),
(3, 0, 2),
(3, 0, 4),
(3, 0, 5),
(3, 1, 0),
(3, 1, 2),
(3, 1, 4),
(3, 1, 5),
(3, 2, 0),
(3, 2, 1),
(3, 2, 4),
(3, 2, 5),
(3, 4, 0),
(3, 4, 1),
(3, 4, 2),
(3, 4, 5),
(3, 5, 0),
(3, 5, 1),
(3, 5, 2),
(3, 5, 4),
(4, 0, 1),
(4, 0, 2),
(4, 0, 3),
(4, 0, 5),
(4, 1, 0),
(4, 1, 2),
(4, 1, 3),
(4, 1, 5),
(4, 2, 0),
(4, 2, 1),
(4, 2, 3),
(4, 2, 5),
(4, 3, 0),
(4, 3, 1),
(4, 3, 2),
(4, 3, 5),
(4, 5, 0),
(4, 5, 1),
(4, 5, 2),
(4, 5, 3),
(5, 0, 1),
(5, 0, 2),
(5, 0, 3),
(5, 0, 4),
(5, 1, 0),
(5, 1, 2),
(5, 1, 3),
(5, 1, 4),
(5, 2, 0),
(5, 2, 1),
(5, 2, 3),
(5, 2, 4),
(5, 3, 0),
(5, 3, 1),
(5, 3, 2),
(5, 3, 4),
(5, 4, 0),
(5, 4, 1),
(5, 4, 2),
(5, 4, 3))
Counting them:
len(permutations)
120
Computing the number directly:
import scipy.special
scipy.special.perm(6, 3)
120.0
4. Permutations of size 2 of \((0, 1, 2, 3, 4, 5, 6)\).
Generating them all:
digits = range(7)
permutations = tuple(itertools.permutations(digits, r=2))
permutations
((0, 1),
(0, 2),
(0, 3),
(0, 4),
(0, 5),
(0, 6),
(1, 0),
(1, 2),
(1, 3),
(1, 4),
(1, 5),
(1, 6),
(2, 0),
(2, 1),
(2, 3),
(2, 4),
(2, 5),
(2, 6),
(3, 0),
(3, 1),
(3, 2),
(3, 4),
(3, 5),
(3, 6),
(4, 0),
(4, 1),
(4, 2),
(4, 3),
(4, 5),
(4, 6),
(5, 0),
(5, 1),
(5, 2),
(5, 3),
(5, 4),
(5, 6),
(6, 0),
(6, 1),
(6, 2),
(6, 3),
(6, 4),
(6, 5))
Counting them:
len(permutations)
42
Computing the number directly:
import scipy.special
scipy.special.perm(7, 2)
42.0
5. Combinations of size 3 of \((0, 1, 2, 3, 4, 5)\).
Generating them all:
digits = range(6)
combinations = tuple(itertools.combinations(digits, r=3))
combinations
((0, 1, 2),
(0, 1, 3),
(0, 1, 4),
(0, 1, 5),
(0, 2, 3),
(0, 2, 4),
(0, 2, 5),
(0, 3, 4),
(0, 3, 5),
(0, 4, 5),
(1, 2, 3),
(1, 2, 4),
(1, 2, 5),
(1, 3, 4),
(1, 3, 5),
(1, 4, 5),
(2, 3, 4),
(2, 3, 5),
(2, 4, 5),
(3, 4, 5))
Counting them:
len(combinations)
20
Computing the number directly:
import scipy.special
scipy.special.comb(6, 3)
20.0
6.Combinations of size 2 of \((0, 1, 2, 3, 4, 5)\).
Generating them all:
digits = range(6)
combinations = tuple(itertools.combinations(digits, r=2))
combinations
((0, 1),
(0, 2),
(0, 3),
(0, 4),
(0, 5),
(1, 2),
(1, 3),
(1, 4),
(1, 5),
(2, 3),
(2, 4),
(2, 5),
(3, 4),
(3, 5),
(4, 5))
Counting them:
len(combinations)
15
Computing the number directly:
import scipy.special
scipy.special.comb(6, 2)
15.0
7. Combinations of size 5 of \((0, 1, 2, 3, 4, 5)\).
Generating them all:
digits = range(6)
combinations = tuple(itertools.combinations(digits, r=5))
combinations
((0, 1, 2, 3, 4),
(0, 1, 2, 3, 5),
(0, 1, 2, 4, 5),
(0, 1, 3, 4, 5),
(0, 2, 3, 4, 5),
(1, 2, 3, 4, 5))
Counting them:
len(combinations)
6
Computing the number directly:
import scipy.special
scipy.special.comb(6, 5)
6.0
Question 3#
3. A class consists of 3 students from Ashville and 4 from Bewton. A committee of 5 students is chosen at random the class.
1. Find the number of committees that include 2 students from Ashville and 3 from Bewton are chosen.
We directly enumerate them:
students = ("Ashville", "Ashville", "Ashville", "Bewton", "Bewton", "Bewton", "Bewton")
committees = tuple(itertools.combinations(students, 5))
committees
(('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Bewton'))
Selecting only the ones with 2 Ashville students (if there are 2 Ashville students then there are 3 Bewton ones):
sum(1 for committee in committees if committee == ("Ashville", "Ashville", "Bewton", "Bewton", "Bewton"))
12
2. In fact 2 students, from Ashville and 3 from Bewton are chosen. In order to watch a video, all 5 committee members sit in a row. In how many different orders can they sit if no two students from Bewton sit next to each other.
To answer this we need to consider committees as permutations (as order matters):
committee = ("Ashville", "Ashville", "Bewton", "Bewton", "Bewton")
seating_arrangements = tuple(itertools.permutations(committee))
seating_arrangements
(('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Ashville', 'Bewton', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Ashville', 'Bewton', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Ashville', 'Bewton', 'Bewton', 'Ashville', 'Bewton'),
('Ashville', 'Bewton', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Ashville', 'Bewton', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Ashville', 'Bewton', 'Ashville', 'Bewton'),
('Bewton', 'Ashville', 'Bewton', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Ashville', 'Ashville', 'Bewton'),
('Bewton', 'Bewton', 'Ashville', 'Bewton', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'),
('Bewton', 'Bewton', 'Bewton', 'Ashville', 'Ashville'))
For no two students from Bewton to site next to each other the order is fixed:
sum(
1
for seating_arrangement in seating_arrangements
if seating_arrangement == ("Bewton", "Ashville", "Bewton", "Ashville", "Bewton")
)
12
Question 4#
4. Three letters are selected at random from the 8 letters of the wordCOMPUTER, without regard to order.
1. Find the number of possible selections of 3 letters.
letters = ("C", "O", "M", "P", "U", "T", "E", "R")
selections = tuple(itertools.combinations(letters, 3))
selections
(('C', 'O', 'M'),
('C', 'O', 'P'),
('C', 'O', 'U'),
('C', 'O', 'T'),
('C', 'O', 'E'),
('C', 'O', 'R'),
('C', 'M', 'P'),
('C', 'M', 'U'),
('C', 'M', 'T'),
('C', 'M', 'E'),
('C', 'M', 'R'),
('C', 'P', 'U'),
('C', 'P', 'T'),
('C', 'P', 'E'),
('C', 'P', 'R'),
('C', 'U', 'T'),
('C', 'U', 'E'),
('C', 'U', 'R'),
('C', 'T', 'E'),
('C', 'T', 'R'),
('C', 'E', 'R'),
('O', 'M', 'P'),
('O', 'M', 'U'),
('O', 'M', 'T'),
('O', 'M', 'E'),
('O', 'M', 'R'),
('O', 'P', 'U'),
('O', 'P', 'T'),
('O', 'P', 'E'),
('O', 'P', 'R'),
('O', 'U', 'T'),
('O', 'U', 'E'),
('O', 'U', 'R'),
('O', 'T', 'E'),
('O', 'T', 'R'),
('O', 'E', 'R'),
('M', 'P', 'U'),
('M', 'P', 'T'),
('M', 'P', 'E'),
('M', 'P', 'R'),
('M', 'U', 'T'),
('M', 'U', 'E'),
('M', 'U', 'R'),
('M', 'T', 'E'),
('M', 'T', 'R'),
('M', 'E', 'R'),
('P', 'U', 'T'),
('P', 'U', 'E'),
('P', 'U', 'R'),
('P', 'T', 'E'),
('P', 'T', 'R'),
('P', 'E', 'R'),
('U', 'T', 'E'),
('U', 'T', 'R'),
('U', 'E', 'R'),
('T', 'E', 'R'))
Counting them:
len(selections)
56
Note that a string is in fact an iterable so we can also do:
letters = "COMPUTER"
selections = tuple(itertools.combinations(letters, 3))
len(selections)
56
2. Find the number of selections of 3 letters with the letterP.
sum(1 for selection in selections if "P" in selection)
21
3. Find the number of selections of 3 letters where the 3 letters form the wordTOP.
sum(1 for selection in selections if sorted(selection) == sorted(("O", "P", "T")))
1