Chapter 12.4, Problem 10E

Exercises 7–12 deal with the poker hands described in Table 12.3. We assume that we are drawing five cards from a standard 52-card deck.

Playing poker. To construct a straight, we must choose five cards in sequence (not all of the same suit).

a. In how many ways can we choose a sequence of five cards?

b. For each sequence in part (a) we must select a suit for the first card, a suit for the second card, and so on. In how many ways can we do this? (Hint: Draw a slot diagram for the five cards.)

c. Multiply the results from parts (a) and (b).

d. Subtract the number of royal flushes and straight flushes that are not royal, found in Exercises 7 and 8.

7. Playing poker. In how many ways can we obtain a royal flush $\left(10,\text{ J, Q, K, and A, all the sae suit?}\right)$

8. Playing poker. In constructing a straight flush, we first choose a suit and then choose a sequence of five cards within the suit.

a. In how many ways can we choose the suit?

b. In how many ways can we choose the sequence of five cards within the suit?

c. In how many ways can we construct a straight flush?