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

Given that 5 cards are drawn out of 52 cards. We know that there are 4 aces present in a deck of 52 cards.

We need to find the no. of ways of drawing 5 cards with exactly one ace out of a deck of 52 cards.

Let us assume the no. of ways of drawing cards be N.

N = (Drawing 1 ace out of 4 aces) × (Drawing 4 cards out of remaining 48 cards)

N = (4C1) × (48C4)

We know that ,

And also n! = (n)(n – 1)......2.1

N = 4 × 194580

N = 778320

The no. of ways of drawing 5 cards with exactly one ace is 778320.

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