Question

How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?

Answer 1

Solution

We need to remember that in a standard deck we have 4 aces and 48 other types of cards

For this case we can solve the problem with the follwoing operation:

$(4C2)\cdot(48C3)=\frac{4!}{2!2!}\cdot\frac{48!}{45!3!}=6\cdot17296=103776$

So then we have 103776 ways to create the combination required