A1, A2,⋯,A30 are 30 sets, each having 5 elements and B1,B2,⋯,Bn are n sets each with 3 elements. If 30⋃i=1Ai=n⋃j=1Bj=S and each element of S belongs to exactly 10 of the Ai 's and exactly 9 of the Bj 's, then the value of n is

A1, A2,⋯,A30 are 30 sets, each having 5 elements and B1,B2,⋯,Bn ar

1.	A1, A2,⋯,A30 are 30 sets, each having 5 elements and B1,B2,⋯,Bn are n sets each with 3 elements. If 30⋃i=1Ai=n⋃j=1Bj=S and each element of S belongs to exactly 10 of the Ai 's and exactly 9 of the Bj 's, then the value of n is
Answer» $A_{1}, A_{2}, \dots, A_{30}$ are $30$ sets, each having $5$ elements and $B_{1}, B_{2}, \dots, B_{n}$ are $n$ sets each with $3$ elements. If $30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S$ and each element of $S$ belongs to exactly $10$ of the $A_{i}$ 's and exactly $9$ of the $B_{j}$ 's, then the value of $n$ is