Question

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

Answer 1

There are total 4 king cards out of 52

we have to select one king from four king

Total no. of ways ${=}^4{C_1}^{48}{C}_4$

$=\frac{4!}{3!}\times \frac{48!}{4!44!}$

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

$=778320$