MATH213 HW 7
Due Wednesday, October 11
Solve five of the six problems below.
1. A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond
croissants, apple croissants, and broccoli croissants. How many ways are there to choose
(a) a dozen croissants?
(b) two dozen croissants with at least two cherry croissants and at least three croissants
of each other kind?
(c) a dozen croissants with at most 3 plain croissants and at least two cherry croissants?
(d) two dozen croissants with exactly 2 cherry croissants, at most 4 plain croissants and
at least 3 apple croissants?
2. How many solutions are there to the inequality
x1+x2+x3≤13,
where x1, x2, and x3are nonnegative integers such that
(a) x1≥2?
(b) x1≤2 and x3≥3?
(Hint: introduce an auxiliary variable x4so that x1+x2+x3+x4= 13.)
3. How many different strings can be made from the letters in MATHEMATICS, using
all letters?
4. How many ways can 30 books be placed on four distinguishable shelves
(a) if all books are indistinguishable copies of the same title?
(b) if all books are distinguishable, and the order of the books on a shelf does NOT
matter?
(c) if 10 books are indistinguishable copies of the same title and all other books are
distinguishable and the order of the books on a shelf does NOT matter?
5. What is the probability that a five-card poker hand contains
(a) a straight, that is, five cards that have consecutive kinds (for example, Q-J-10-9-8)?
(b) two pairs, that is, two of each of two different kinds and a fifth card of a third kind?
6. # 38 on Page 362.
