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 = (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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