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Q.

Suppose A1,A2,A3,.. , 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=S and each elements 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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answer is 45.

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Detailed Solution

O(S)=O∪i=130 Ai=110(5×30)=15Since, element in the union S belongs to 10 of Ai′sAlso, O(S)=O∪j=1n Bj=3n9=n3∴n3=15⇒n=45 Ans.
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