Try this problem from Test of Mathematics, TOMATO Objective problem number 44, useful for ISI B.Stat and B.Math.

**Problem: TOMATO Objective 44**

Suppose that (n> 2) are real numbers such that x for . Consider the sum where the summations are taken over all i, j, k: and i, j, k are all distinct. Then S equals:

**(A)** ; **(B)** (n-3)(n-4); **(C)** (n-3)(n-4)(n-5); **(D)** none of the foregoing expressions;

**Discussion:**

Since

Hence

Since and

Therefore

Hence option D

## Some Useful Links:

How to use invariance in Combinatorics – ISI Entrance Problem – Video

Google