Question

Find the number of
(i)diagonals
(ii)triangles

formed in a decagon.

Answer 1

(i) ${}^{10}{C}_2$ - 10 = 45 - 10 = 35
(ii) ${}^{10}{C}_3$ = $\frac{10!}{3!7!}$ = $\frac{10\times 9\times 8}{6}$ = 120.