Suppose A1,A2,A3,⋯,A30 are thirty sets each having 5 elements and B1,B2,⋯,Bn are n sets each with 3 elements. Let ⋃30i−1Ai=⋃nj−1Bj=S and each element of S belongs to exactly 10 of the A′is and exactly 9 of the B′js. Then n is equal to

Suppose A1,A2,A3,⋯,A30 are thirty sets each having 5 elements and

1.	Suppose A1,A2,A3,⋯,A30 are thirty sets each having 5 elements and B1,B2,⋯,Bn are n sets each with 3 elements. Let ⋃30i−1Ai=⋃nj−1Bj=S and each element of S belongs to exactly 10 of the A′is and exactly 9 of the B′js. Then n is equal to
Answer» Suppose $A_{1}, A_{2}, A_{3}, \dots, A_{30}$ are thirty sets each having 5 elements and $B_{1}, B_{2}, \dots, B_{n}$ are n sets each with 3 elements. Let $⋃_{i - 1}^{30} A_{i} = ⋃_{j - 1}^{n} B j = S$ 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