practice problems pending

Q1. 

Find the number of triangles whose angular points are at the angular points of a given polygon of (n) sides, but none of its sides are the sides of the polygon.

S1.
Simple application of Kaplansky's first lemma.

Formula derived is:
(n-k-1)C(k-1) + (n-k)C(k)
Here k = 3
(n-4)C(2) + (n-3)C(3)
= (n-4)(n-5)/2 + (n-3)(n-4)(n-5)/6
= (n-4)(n-5)/2[1 + (n-3)/3]
= n(n-4)(n-5)/6

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