Mathematics - Permutation & Combination Question with Solution | TestHub

Suppose $A_1,A_2,A_3,\dots A_{30}$ are thirty sets each with five elements and $B_1,B_2,B_3,\dots .B_n$ are n sets each with three elements such that ${\bigcup }_{i=1}^{30}{A}_i={\bigcup }_{i=1}^n{B}_i=S$. If each element of S belongs to exactly ten of the $A_i$ 's and exactly 9 of the $B_i$ 's then the value of n is