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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 3S0 i=1 Ai = nS i=1 Bj = S and each elements of S belongs to exactly 10 of the Ais and exactly 9 of the Bjs. Then, n is equal to
Dear student Since, each Ai has 5 elements, we havesum from i=1 to 30 n(Ai) = 5*30 = 150 Let set S consists of k elements.Since, each elements in S belongs to exactly 10 of Ai'sTherefore,sum from i = 1 to 30 n(Ai) = 10k Hence 10k = 150 k = 15 Now, since each Bj has 3 elements and each S belongs to exactly 9 of Bj'sTherefore,n(Bj) = 9k 3n = 9k = 9*15 n = 45
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