Question

Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Answer 1

There are total 4 aces in the deck of 52 cards. So, we are left with 48 cards.
∴ Required ways = ${}^4{C}_1{\times }^{48}{C}_4=\frac{4}{1}\times \frac{48}{4}\times \frac{47}{3}\times \frac{46}{2}\times \frac{45}{1}=778320$