Question

A set contains $(2n+1)$ elements. Find the number of subsets of the set which constants at most $n$ elements.

Answer 1

Number of elements in set $=2n+1$

Number of subsets which almost contain $n$ elements ${=}^{2n+1}{c}_n$

$=\frac{(2n+1)!}{n!(n+1)!}$