Two-Ace Hands

Choose 2 of the 4 aces, then fill the rest of the hand from non-aces.

There are 48 non-ace cards.

1. 1. Choose the aces

   $\left(\genfrac{}{}{0ex}{}{4}{2}\right)$ ways to choose 2 aces from 4.

2. 2. Choose the rest

   $\left(\genfrac{}{}{0ex}{}{48}{3}\right)$ ways to choose the remaining 3 cards from the 48 non-aces.

3. 3. Multiply

   Total is $\left(\genfrac{}{}{0ex}{}{4}{2}\right)\left(\genfrac{}{}{0ex}{}{48}{3}\right)=6\times 17296=103776$.

   $$\left(\genfrac{}{}{0ex}{}{4}{2}\right)\left(\genfrac{}{}{0ex}{}{48}{3}\right)=103776$$

Answer: C(4,2) * C(48,3)