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

If elements are not repeated, then number of elements in A1∪A2∪A3∪…∪A30 is 30×5. But each element isused 10 times, soS=30×510=15----iSimilarly, if elements in B1,B2,…,Bn are not repeated, then total number of elements is 3n but each element isrepeated 9 times, soS=3n9⇒15=3n9    from Eq. (i)⇒n=45