Math Help - show this

1. show this

Can someone pls show that

nCr = n(n-1)(n-2) ... (n-r+1)
r(r-1)*...*2*1

$_nC_r = \frac{n!}{r!(n-r)!} = \frac{n(n-1)..(n-r+1)(n-r)..(1)}{r!(n-r)!}$ $=\frac{n(n-1)..(n-r+1)r!}{r!(n-r)!}=\frac{n(n-1)..(n-r+1)}{r!}$
Choosing $r$ from $n$ distinct elements, the first may be choosen in $n$ ways the second in $(n-1)$ down to the $r$-the in $(n-r+1)$ ways, so there are $n(n-1)..(n-r+1)$ ways of doing the selection, but as each combination appears in these choices in ever permutation we are counting each combination r! times so the number of combinations is:
$\frac{n(n-1)..(n-r+1)}{r!}$