Problem 4. Proving binomial identities via counting

4 points possible (graded)Binomial identities (i.e., identities involving binomial coefficients) can often be proved via a counting interpretation. For each of the binomial identities given below, select the counting problem that can be used to prove it.

Hint: You may find it useful to review the lecture exercise on counting committees before attempting the problem.

(You need to answer all 4 questions before you can submit.)

\f\f\f\f