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