Solve the problem.
-A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four cards of one suit and one card of another suit?
A)37,180
B)9295
C)111,540
D)715

Question

Solve the problem.
-A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four cards of one suit and one card of another suit? 
A)37,180
B)9295
C)111,540
D)715

Quizplus · Accepted Answer

The number of ways to choose a suit for the four cards is 4 (since there are 4 suits). For each of these choices, there are $ \binom{13}{4} $ ways to choose the four cards from the chosen suit. Then, there are 48 remaining cards (from the other three suits), and $ \binom{48}{1} $ ways to choose one card from these. So, the total number of different hands is $ 4 \times \binom{13}{4} \times \binom{48}{1} = 4 \times 715 \times 48 = 111,540 $.

Solve the Problem. -A Poker Hand Consists of 5 Cards Dealt from an Dealt