8 choose 3 + 8 choose 5

8 choose 3 + 8 choose 5

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

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