Question

Find the number of 5 card combination out of a deck of 52 cards if there is exactly one ace in each combination.

• A. $4321$
• B. $5647$
• C. $4512$
• D. $3268$

Answer 1

Answer: (C)

$4512$

We need 5 cards so in that exactly three should be ace

So first, one ace need to to be selected out of 4 $⟹(\frac{4}{1})$ ways

after that we need to select two cards out 48 cards(These are not aces) $⟹(\frac{48}{2})$ ways

Total ways we will get a 5 card combinations is $(\frac{4}{1})(\frac{48}{2})=4\times \frac{48\times 47}{2}=4512$ ways