Suppose .$$A1$$,$$A2$$,…,$$A30$$ are thirty sets each having $$5$$ elements and $$B1$$,$$B2$$,…,Bn are n sets each having $$3$$ elements. let ∪$$i=130Ai=$$∪$$j=1n$$ $$Bj=S$$ and each elements of S belongs to exactly $$10$$ of Ai' s and exactly $$9$$ of Bi ' s The value of n is equal to

Question

Suppose .$$A1$$,$$A2$$,…,$$A30$$ are thirty sets each having $$5$$ elements and $$B1$$,$$B2$$,…,Bn are n sets each having $$3$$ elements. let ∪$$i=130Ai=$$∪$$j=1n$$ $$Bj=S$$ and each elements of S belongs to exactly $$10$$ of Ai' s and exactly $$9$$ of Bi ' s The value of n is equal to