#### Question

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

#### Solution

From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king.

In a deck of 52 cards, there are 4 kings.

1 king can be selected out of 4 kings in `""^4C_1` ways.

4 cards out of the remaining 48 cards can be selected in `""^48C_4` ways.

Thus, the required number of 5-card combinations is `""^4C_1 xx ""^48C_4`

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Solution Determine the Number of 5-card Combinations Out of a Deck of 52 Cards If Each Selection of 5 Cards Has Exactly One King. Concept: Concept of Combinations.