(a) Give a combinatorial proof that if n is an odd integer, then the number of ways...

(a) Give a combinatorial proof that if n is an odd integer, then the number of ways to select an even number of objects from a set of n objects is equal to the number of ways to select an odd number of objects.

(b) Give a combinatorial proof of Vandermonde’s identity: For 0 ≤ r ≤ n + m,

(c) Prove that