Answer
$32$
Work Step by Step
$\binom{a}{b}=\binom{a}{a-b} $
$ \binom {5}{0}=\binom {5}{5}$
$ \binom {5}{1}=\binom {5}{4}$
$ \binom {5}{2}=\binom {5}{3}$
$ \binom {5}{0}+\binom {5}{1}+ \binom {5}{2}+\binom {5}{3}+\binom {5}{4}+\binom {5}{5}=2\times (\binom {5}{0}+\binom {5}{1}+ \binom {5}{2})=2\times \left( \dfrac {5!}{0!\left( 5-0\right) !}+\dfrac {5!}{1!\left( 5-1\right) !}+\dfrac {5!}{2!\left( 5-2\right) !}\right) =2\times \left( 1+5+\dfrac {3!\times 4\times 5}{3!\times 2!}\right) =2\times \left( 1+5+10\right) =32 $
