Question: Problem 3: Recall that the binomial coefficients are defined by n! n(n - 1) . ..(n - k+ 1) k!(n - k)! k! (a) Prove

Problem 3: Recall that the binomial coefficients are defined by n! n(n - 1) . ..(n - k+ 1) k!(n - k)! k! (a) Prove the identity (") = (#) + (x",). (This can be proven either using the formula, or using the fact that (") counts the number of ways to choose k things from a set of n. Both ways are fine!) (b) Using part (a) and induction prove the binomial formula n (x ty)" = ) for n E N

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