Q29 of 58 Page 12

Suppose A1, A2, ..., A30 are thirty sets each having 5 elements and B1, B2, ..., Bn are n sets each with 3 elements, let union _ i = 1 ^30a_i = union _ j = 1 ^nb_j = s and each element of S belongs to exactly 10 of the Ai’s and exactly 9 of the B,’S. then n is equal to

Given:


To find: value of n


Since elements are not repeating, number of elements in A1∪ A2∪ A3∪ ………∪ A30 is 30 × 5


But each element is used 10 times


So, 10 × S = 30 × 5


⇒ 10 × S = 150


⇒ S = 15


Since elements are not repeating, number of elements in B1∪ B2∪ B3∪ ………∪ Bn is 3 × n


But each element is used 9 times


So, 9 × S = 3 × n


⇒ 9 × S = 3n




⇒ n = 45


Hence, the value of n is 45

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