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 $=\frac{12 !}{4 ! 8 !}=495$