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

Question:

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.

$\therefore$ 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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