Tough general proving problem

[Johncena]

For k>=1 where k is a positive integer, C_k = {1,2,3.....,k-1,k}. Let F be a set of subsets of C_{k .} If no element of F is a subset of another element of F, we call it a special set

If F is a special set, and let a_k cv be the number of elements of F that have exactly k integers.
Prove,
(a₀)/ⁿC₀ + (a₁)/ⁿC₁ +.......... +(a_n)/ⁿC_n <=1

2. For each positve integer k, determine the number of elements in the largest special set of C_k.

PLease give me general guideline on how to solve these