Question

Let S = {1, 2, 3, ...., n}. If x denotes the set of all subsets of S containing exactly two elements, then the value of is given by

Answer 1

\frac{n(n-1)}{2}

Answer 2

The problem asks for the number of subsets of a set S with 'n' elements, where each subset must contain exactly two elements. This is a combination problem, as the order of elements within a subset does not matter. The number of ways to choose 2 elements from 'n' distinct elements is given by the combination formula $\binom{n}{2}$, which simplifies to $\frac{n(n-1)}{2}$.