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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.
∴ 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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