Tag: Factorials

Compute some binomial coefficients

by RoRi

Compute the following:

$\displaystyle{ \binom{5}{3} = \frac{5!}{3! \ 2!} = 10}.$
$\displaystyle{ \binom{7}{0} = \frac{7!}{7! \ 0!} = 1}.$
$\displaystyle{ \binom{7!}{6!1!} = \frac{7!}{6! \ 1!} = 7}.$
$\displaystyle{ \binom{7}{2} = \frac{7!}{5! \ 2!} = 21}.$
$\displaystyle{ \binom{17}{14} = \frac{17!}{14! \ 3!} = 680}.$
$\displaystyle{ \binom{0}{0} = \frac{0!}{0! \ 0!} = 1}.$