Choose(n,k) is maximum at (n/2) if n is even or at (n-1)/2 and (n+1)/2 if odd
Choose(n,k) is monotonic increasing to this maximum and monotonic decreasing after it
so, for a given n, the farther away k is from the midpoint the smaller it is
That answers (a) and (b) w/o computation.
I don't quite get (c). Are you saying you want to express Choose(100,95) in terms of Choose(99,4) ?