Question

In the answer from Part I, each two-ace hand got counted twice. For example, A A X got counted as a separate hand from A A X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?

Answer 1

Assuming exactly 3 cards are being drawn: we want 2 of them to come from the 4 available aces, and the last 1 to come from the remaining 48 non-ace cards.

`\dbinom42\cdot\dbinom{48}1=(4!)/(2!(4-2)!)\cdot(48!)/(1!(48-1)!)=6\cdot48=288`