Mathematics for Computer Science

14.11. References 607

Problems for Section 14.7

Practice Problems

Problem 14.33.
Indicate how many 5-card hands there are of each of the following kinds.

(a)ASequenceis a hand consisting of five consecutive cards of any suit, such as

5 ~ 6 ~ 7  8  9 |:

Note that an Ace may either be high (as in 10-J-Q-K-A), or low (as in A-2-3-4-5),
but can’t go “around the corner” (that is, Q-K-A-2-3 isnota sequence).

How many differentSequencehands are possible?

(b)AMatching Suitis a hand consisting of cards that are all of the same suit in
any order.

How many differentMatching Suithands are possible?

(c)AStraight Flushis a hand that is both aSequenceand aMatching Suit.

How many differentStraight Flushhands are possible?

(d)AStraightis a hand that is aSequencebut not aMatching Suit.

How many possibleStraightsare there?

(e)AFlushis a hand that is aMatching Suitbut not aSequence.

How many possibleFlushesare there?

Class Problems

Problem 14.34.
Here are the solutions to the next 7 short answer questions, in no particular order.
Indicate the solutions for the questions and briefly explain your answers.

1:

nŠ

.nm/Š

2:

nCm

m

!

3: .nm/Š 4: mn

5:

n 1 Cm

m

!

6:

n 1 Cm

n

!

7: 2mn 8: nm

(a)How many lengthmwords can be formed from ann-letter alphabet, if no letter
is used more than once?