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

Explanation

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)** 4_(C_1)`

`=>(48!)/(4!**44!)**(4!)/(1!**3!)`

`=>(48**47**46**45)/(4**3**2)**4`

`=>778320`