# Determine the Number of 5 Cards Combinations Out of a Deck of 52 Cards If There is Exactly One Ace in Each Combination. - Mathematics

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

#### Solution

There are total 4 aces in the deck of 52 cards. So, we are left with 48 cards.
∴ Required ways = ${}^4 C_1 \times^{48} C_4 = \frac{4}{1} \times \frac{48}{4} \times \frac{47}{3} \times \frac{46}{2} \times \frac{45}{1} = 778320$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 26 | Page 16