# Q.8.    Determine the number of 5-card combinations out of a deck of 52 cards if each            selection of 5 cards has exactly one king.

S seema garhwal

From a deck of 52 cards, 5 cards combinations have to be made in such a way that in each selection of 5 cards there is exactly 1 king.

Number of kings =4

Number of ways of selecting 1 king $=^4C_1$

4 cards from the remaining 48 cards are selected in $^4^8C_4$ ways.

Thus, the required number of 5 card combinations $=^4C_1 .^4^8C_4$

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