Suppose \( A_{1}, A_{2}, A_{3}, \ldots \ldots, A_{30} \) are thirty...

Suppose \( A_{1}, A_{2}, A_{3}, \ldots \ldots, A_{30} \) are thirty sets each having 5 elements and \( B_{1}, B_{2}, \ldots \ldots ., B_{n} \) are \( n \) sets each with 3 elements.
P
Let \( \bigcup_{i=1}^{30} A_{i}=\bigcup_{j=1}^{n} B_{j}=S \) and each elements of \( S \) belongs to
W. exactly 10 of the \( A^{\prime} s \) and exactly 9 of the \( B_{j}^{\prime} s \). Then \( n \) is equal to
(a) 15
(b) 3
(c) 45
(d) None of these