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

Question

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

Infinity Learn · Accepted Answer

$$S=$$∪$$i=130$$ Ai, so $$n(S)=110(5$$×$$30)=15$$  (since$$ element in the union S belongs to exactly $$10$$ of the Ai ’$$s).  Again , $$S=$$∪$$i=1n$$ Bi so $$n(S)=1/9(3$$×$$n)=n/3=15$$⇒$$n=45$$

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Suppose A1, A2, ….., A30 are thirty sets each having 5 elements and B1, B2 ………, Bn are n sets each with 3 elements, let ∪i=130 Ai=∪j=1n Bj=Sand each element of S belongs to exactly 10 of the Ai ’s and exactly 9 of the Bj ’s. Then n is equal to

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