Question

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

Answer 1

We have,

Number of cards in a deck = 52.

If 52 cards, there are 4 aces and 48 other cards, (∵ 4 + 48 = 52). 

If there is exactly one ace in each 5 card combination, then one ace out of 4 can be selected in ⁴C₁ ways and 4 non-ace cards can be selected out of 48 in ⁴⁸C₄ ways. 

∴ Required number of combination = ⁴C₁ x ⁴⁸C₄

= 4/1 x (48 x 47 x 46 x 45)/(4 x 3 x 2 x 1) = 778320