Discrete Mathematics

Question

Let B be a subset of A. Let A = n and B = k. What is the number of

subsets of A whose intersection with B has 3 elements?

Answer 1

A subset of A has 3 of the k elements of B, so it has C(k, 3) combinations. Then, for the n-k elements not in B, each can be in the subset or not, so there are 2^n-k possibilities. Thus, there are

C(k, 3)2^n-k subsets of A that have 3 elements in B.