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,
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,
There will be as many ways of choosing $4$ cards from $52$ cards as there are combinations of $52$ different things, taken $4$ at a time. Therefore
The required number of ways $=\,\,^{52} C _{4}=\frac{52 !}{4 ! 48 !}=\frac{49 \times 50 \times 51 \times 52}{2 \times 3 \times 4}$
$=270725$
There are $12$ face cards and $4$ are to be selected out of these $12$ cards. This can be done in $^{12} C _{4}$ ways.
Therefore, the required number of ways $=\frac{12 !}{4 ! 8 !}=495$
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