Question

Determine the number of combinations out of deck of 52 cards of each selection of 5 cards has exactly one ace.

Answer 1

Number of cards in a deck = 52

Total number of aces = 4

Hence Number of remaining cards = 52 – 4 = 48

We have to make a collection of 5 cards, in which there is 1 ace and 4 other cards.

Hence, number of ways choosing 1 out of 4 ace.

Now,Number of ways choosing 4 cards out of 48 cards

Hence, total number of collection having 5 cards

Total number of collection having 5 cards

= ⁴C₁ × ⁴⁸C₄ = 4 × 194580 = 778320

Hence, number of combinations formed by 5 cards = 778320.