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.

Answer 1

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 4C1 ways.
4 cards out of the remaining 48 cards can be selected in 48C4 ways.
Thus, the required number of 5-card combinations is $^4C_1\times\space^{48}C_4.$