Question

What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these are face cards.

Answer 1

We have,

Number of ways of choosing $4$ cards from a pack of $52$ cards is the number of combinations of $52$ different things taken $4$ at time

$\therefore$ Required number of ways ${=}^{52}{C}_4$

$=\frac{52\times 51\times 50\times 49}{4\times 3\times 2\times 1}=270725$

Face card means Kings, Queen , Jack there are $4$ suits, each suit has $3$ face cards.

Therefore there are $12$ face cards and $4$ are to be selected out of $12$ cards, in ${}^{12}{C}_4$ ways

Required number of ways ${=}^{12}{C}_4$

$=\frac{12\times 11\times 10\times 9}{4\times 3\times 2\times 1}=495$