counting

Question

How many triangles can be drawn from N given points on a circle?
(a) N! (b) 3!
(c) N! / 3! (d) (N – 1)N(N – 2)/6

Answer 1

Each set of 3 of the N points determines a triangle, and each triangle is determined in this way, so all you have to do is determine how many 3 element subsets a set of N things has. 

so no. of triangle's = ⁿC₃

= n(n-1)(n-2)/6

Answer 2

(d) required no. of ways= ^NC₃= N(N-1)(N-2)/6.

Answer 3

ⁿc₃   triangles can be drawn from N given points on a circle.