Chapter 14 Cardinality Rules620
(e)LetHSFbe the set of all straight flush hands; that is, the hand is both a straight
and a flush.
What isjHSFj?
(f)LetHHCbe the set of all high-card hands; that is, hands that do not include
pairs, are not straights, and are not flushes.
What isjHHCj?
Problems for Section 14.10
Practice Problems
Problem 14.59.
Prove the following identity by algebraic manipulation and by giving a combinato-
rial argument:
n
r
!
r
k!
D
n
k!
n k
r k!
Problem 14.60.
Give a combinatorial proof for this identity:
XiCjCkDn
i;j;k 0n
i;j;k!
D 3 nClass Problems
Problem 14.61.
According to the Multinomial theorem,.wCxCyCz/ncan be expressed as a
sum of terms of the form
n
r 1 ;r 2 ;r 3 ;r 4!
wr^1 xr^2 yr^3 zr^4 :(a)How many terms are there in the sum?(b)The sum of these multinomial coefficients has an easily expressed value. What