Question

How many 4 card hands that contain exactly 3 aces and 1 queen can be chosen from a 52 card deck?

Answer 1

There are 16 possible hands.

Choosing 3 aces from 4 possible is expressed by:

4C3 = 4!/3! 1! = 4

Choosing 1 queen from 4 possible is expressed by:

4C1 = 4!/1! 3! = 4

This gives us 4*4 = 16 possible hands.