8 choose 3 + 8 choose 5

8 choose 3 + 8 choose 5

$${ 8 \choose 3 } + { 8 \choose 5 } = 2 { 8 \choose 3 } = 2{ 8 \choose 5 } = 112$$

$$2 { 8 \choose 3 }
=2*\left(
\frac{8!}{3!(8-3)!}
\right)
=2*\left(
\frac{8!}{3!5!}
\right)
=2*\left(
\frac{5!*6*7*8}{3!5!}
\right)
=
2*\left(
\frac{6*7*8}{3!}
\right)\\\\
=
2*\left(
\frac{336}{6}
\right)
=
\frac{336}{3} =112$$