Question

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination

Answer 1

Total number of cards in a pack 52

Number of aces = 4

Number of cards to be selected = 5

The number of ways of selecting 3 aces from 4 aces is 4C₃

The number of ways of selecting the remaining 2 cards
from the remaining 48 cards (52 – 4 aces cards) = 48C₂

∴ Required number of ways of selection

= 4C₃ × 48C₂

= 4C₁ × 48C₂ 

= `4 xx (48 xx 47)/(2 xx 1)`

= 4 × 24 × 47

= 4512