Question

Suppose A₁, A₂, ..., A₃₀ are thirty sets each having 5 elements and B₁, B₂, ..., B_n are n sets each with 3 elements, let ∪A_i(for i=1 to 30)=∪B_j(for j=1 to n)=S and each element of S belongs to exactly 10 of the A_i’s and exactly 9 of the B_j’S. then n is equal to

(A) 15 

(B) 3 

(C) 45

(D) 35

Answer 1

Answer is (C)