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Determine the number of 5 card combinations out of a deck of 5

Question

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

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Determine the number of

5

card combinations out of a deck of

52

cards if there is exactly one ace in each combination.

11 mins ago

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11 mins ago

Text solutionVerified

In a deck of

52

cards, there are

4

aces.

A combination of

5

cards have to be made in which there is exactly one ace.

Then, one ace can be selected in

^{4} C_{1}

ways and the remaining

4

cards can be selected out of the

48

cards in

^{48} C_{4}

ways.

Thus, by multiplication principle, required number of

5

card combinations

=^{48} C_{4} \times^{4} C_{1}

= \frac{48 !}{4 ! ( 44 )!} \times \frac{4 !}{1 ! 3 !}

= \frac{48 \times 47 \times 46 \times 45}{4 \times 3 \times 2 \times 1} \times 4

= 778320

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Question Text	Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.
Answer Type	Text solution:1
Upvotes	151