In how many ways can a hand consisting of 4 spades, 3 hearts, 2 clubs, and 1 diamond be selected from a deck of 52 cards?
A)86,248,800
B)464,199,736
C)207,352,860
D)3,421,322,190
E)9,425,130

Question

In how many ways can a hand consisting of 4 spades, 3 hearts, 2 clubs, and 1 diamond be selected from a deck of 52 cards? ​
A)86,248,800
B)464,199,736
C)207,352,860
D)3,421,322,190
E)9,425,130

Quizplus · Accepted Answer

We can choose 4 spades out of 13 in 13 choose 4 ways. Similarly, we can choose 3 hearts out of 13 in 13 choose 3 ways, 2 clubs out of 13 in 13 choose 2 ways, and 1 diamond out of 13 in 13 choose 1 way. Therefore, the total number of ways to choose the hand is:

(13 choose 4) * (13 choose 3) * (13 choose 2) * (13 choose 1) = 207,352,860

Therefore, the best choice is C.

In How Many Ways Can a Hand Consisting of 4