Suppose A1,A2,...,A30 are thirty sets each having 5 elements and B1,B2,...,Bn are n sets each with 3 elements. Let ∪i=130Ai=∪j=1nBj=S and each element of S belong to exactly 10 of the Ai's and exactly 9 of the Bj's, then n is equal to(a) 15 (b) 3 (c) 45 (d) 35

Suppose A1,A2,...,A30 are thirty sets each having 5 elements and B1,B2

1.	Suppose A1,A2,...,A30 are thirty sets each having 5 elements and B1,B2,...,Bn are n sets each with 3 elements. Let ∪i=130Ai=∪j=1nBj=S and each element of S belong to exactly 10 of the Ai's and exactly 9 of the Bj's, then n is equal to(a) 15 (b) 3 (c) 45 (d) 35
Answer» Suppose $A_{1}, A_{2}, . . ., A_{30}$ are thirty sets each having 5 elements and $B_{1}, B_{2}, . . ., B_{n}$ are n sets each with 3 elements. Let $\cup_{i = 1}^{30} A_{i} = \cup_{j = 1}^{n} B_{j} = S$ and each element of S belong 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