CS 3333 Mathematical Foundations
Spring '12
| Homework 7 |
Assigned on: 3/21 |
Due: 3/28 |
Solve the following problems from the textbook [KR]. Binomial
coefficients, Pages 421-422: 3 (do
this for [x+y]8), 6, 8, 12, 14, 22, 23 (give combinatorial
argument), 28, 33 [use 8x10 grid; that is, find path from (0,0) to (7,9)].
Generalized permutations and combinations, Pages 432-434: 4, 10, 12, 14, 16,
17, 20, 24, 32, 37, 58, 66. Pages 441-442: 21, 29, 35, 37, 38, 39.
Extra Problems
- Show that C(2n, n) + C(2n, n-1) = C(2n+2, n+1)/2. [Hint: Apply Pascal's
identity followed by the combinatorial identity in problem 23, page 422, to
the expression on the left hand side.]
- Use the above result to give an alternate proof for problem 25, page
422. [Hint: take the right hand side of the identity in this problem, expand
it using Vandermonde's identity, and apply the result from Extra Problem 1.]
|