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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a
15
b
3
c
45
d
none of these
answer is C.
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Detailed Solution
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