There are 4 Ace cards in a deck of 52 cards.
According to the given, we need to select 1 Ace card out of the 4 Ace cards
∴ The number of ways to select 1 Ace from 4 Ace cards is 4C1
⇒ More 4 cards are to be selected now from 48 cards (52 cards – 4 Ace cards)
∴ The number of ways to select 4 cards from 48 cards is 48C4
Number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination = 4C1 × 48C4
= 4 × [48!/(44! 4!)]
= 4 × [(48 × 47 × 46 × 45 × 44!)/ (44! × 24)]
= 4 × 2 × 47 × 46 × 45
= 778320