Given: a deck of 52 cards

There are 4 Ace cards in a deck of 52 cards.

According to question, we need to select 1 Ace card out the 4 Ace cards

∴ No. 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)

∴ No. Of ways to select 4 cards from 48 cards is ⁴⁸C₄

∴ Total number of ways = ⁴C₁ × ⁴⁸C₄

⇒ ⁴C₁ × ⁴⁸C₄ =

⇒ ⁴C₁ × ⁴⁸C₄ =

∴ Number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination 778320.