Discrete Math/Comp Sci... answer with clear explanation please. thanks in advance!

A permutation of length n is a rearrangement of the numbers {1, 2, ....., n}. A permutation is called a mountain permutation if the numbers reading from left to right first increase and then decrease. For example, the permutation 1 2 3 5 7 6 4 is a mountain permutation of length 7, and 2 5 4 3 1 is a mountain permutation of length 5. We also consider increasing permutations of the form 12 3 ...... n and decreasing permutations of the form n ........ 3 2 1 to be mountain permutations. For example, 1 2 3 4 and 4 3 21 are mountain permutations of length 4. (b) Prove the following identity by interpreting it combinatorially in the context of mountain permutations. That is, what is each side counting in terms of mountain permutations, and why are those the same? Sigma^n _k=1 (n - 1 k - 1) = 2^n-1 (c) How many bits (0's and 1's) are required to represent a mountain permutation of length n? Simplify your