11. The following identity is known as Fermat's combinatorial identity.

-

$$

\binom{n}{k} = \sum_{i=k}^{n} \binom{i-1}{k-1}

$$

n = k Give a combinatorial argument (no computations are needed) to establish this identity.

HINT: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest-numbered member?