Find the number of ways to get the following card combinations from a 52-card deck.
-Three of one kind and two of another kind (such as three aces and two nines)
A)44,928 ways
B)24 ways
C)3744 ways
D)1872 ways

Question

Quizplus · Accepted Answer

To get three of one kind and two of another kind (a full house) in a 52-card deck, you first choose the rank for the three of a kind (13 options), then choose 3 out of the 4 suits for those cards (combinations of 4 taken 3 at a time, which is 4), then choose the rank for the pair (12 remaining options, since one rank is already used for the three of a kind), and finally choose 2 out of the 4 suits for the pair (combinations of 4 taken 2 at a time, which is 6). The total number of ways is $13 \times 4 \times 12 \times 6 = 3744$.

Find the Number of Ways to Get the Following Card