Write a proof by induction for the following theorems: 10" 1 9 a) 111 1 n1's b) 2n > n c) Pn, k + 1) = (n k)P(n, k), a recursive relationship about k-permutations. Hint: the recursive step goes from k to k + 1. Explain your solution (premises, axioms and theorems you used) and write all your work to get full credit.