Question

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

Answer 1

There are 4 aces and 48 other cards in a deck of 52 cards. We have to select 1 ace out of 4 aces and 4 other cards out of 48 other cards.

$\therefore$ Number of ways of selection = ${}^4{C}_1{\times }^{48}{C}_4$

= $\frac{4\times 3!}{3!}\times \frac{48\times 47\times 46\times 45\times 44!}{4\times 3\times 2\times 44!}$

= $778320.$