Answer
$495$
Work Step by Step
$C(n,r)=\displaystyle \frac{n!}{(n-r)!r!}$.
Factorials:
$n!=n(n-1)!=n(n-1)(n-2)!=...$
$n!=n(n-1)(n-2)\cdots(3)(2)(1)$
$ 0!=1,\qquad$ by definition.
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$C(12,4)=\displaystyle \frac{12!}{(12-4)!4!}=\frac{12\times 11\times 10\times 9\times(8!)}{(8!)\cdot 4!}$
$=\displaystyle \frac{[12]\times 11\times(10)\times 9}{[4\times 3]\times(2)\times 1}$
$=11\times 5\times 9$
= $495$