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.