Q. 265.0( 2 Votes )

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

Answer :

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 = (^{4}C_{1}) × (^{48}C_{4})

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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