CS 3333 Mathematical Foundations
Spring '12
| Homework 6 |
Assigned on: 3/7 |
Due by: 3/21 |
Solve the following problems from the textbook [KR].
Show all major steps in your solution and give the answer in permultations
and combinations notations or, if explicitly asked, in factorials. Calculating
the final value is optional unless explicitly asked.
Permutations and combinations: Pages 413-415: 3, 4, 5 (give the answers in
factorials),
6 (give the answers in factorias and compute the final numerical value), 7, 9
(no ties), 11, 13, 15,
16 (consider subsets with exactly 1 element, 3 elements, 5 elements, 7 elements
or 9 elements),
17 (use indirect counting --- subtract the number of 0, 1, and 2 element subsets
from the total number of subsets),
18, 19, 22, 24, 25, 26, 28 (think of 40-bit strings with 0 for False and 1 for
True), 30, 34, 35, 38,
41 (rotational symmetry; several permutations give the same seating arrangement
if they can be rotated), 42, and
43 (consider three
disjoint possibilities: three horses tie for the first position, two of the
three horses tie for the first or second positions, and no ties).
Pages 441-443: 20, 22, 23, 24. |