Math 475 Text: Brualdi, Introductory Combinatorics 5th Ed.
Prof: Paul Terwilliger
Selected solutions for Chapter 2
1. Case ∅. Fill in the blanks:
# choices : 5 5 5 5
The answer is 5
4
.
Case {a}. Fill in the blanks left to right:
# choices : 5 4 3 2
The answer is 5 × 4 × 3 × 2 = P (5, 4) = 120.
Case {b}. Fill in the blanks:
# choices : 5 5 5 2
The answer is 5 × 5 × 5 × 2 = 250.
Case {a, b}. Fill in the blanks right to left:
# choices : 2 3 4 2
The answer is 2 × 3 × 4 × 2 = 48.
2. We proceed in stages:
stage to do # choices
1 order the suits 4!
2 order the ranks for suit 1 13!
3 order the ranks for suit 2 13!
4 order the ranks for suit 3 13!
5 order the ranks for suit 4 13!
The answer is 4! × (13!)
4
.
3. If we count the order in which the cards are dealt, the answer is P (52, 5). The number of
different poker hands is
52
5
.
4. (a) Each divisor has the form 3
r
× 5
s
× 7
t
× 11
u
where
0 ≤ r ≤ 4, 0 ≤ s ≤ 2, 0 ≤ t ≤ 6, 0 ≤ u ≤ 1.
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