Inclusion-Exclusion Principle

Suppose $P_1,P_2,\dots,P_{30}$ are thirty sets each having $5$ elements and $Q_1,Q_2,\dots,Q_n$ are $n$ sets with $3$ elements each. Let $\bigcup_{i=1}^{30}P_i=\bigcup_{j=1}^{n}Q_j=S$ and each element of $S$ belongs to exactly $10$ of the $P$’s and exactly $9$ of the $Q$’s. Then $n$ equals

$A_1, A_2, A_3, A_4$ are subsets of $U$ (75 elements). Each $A_i$ has 28 elements. Any two intersect in 12 elements. Any three intersect in 5 elements. All four intersect in 1 element. Find the number of elements belonging to none of the four subsets.