Suppose A1,A2,.........A30 are 30 sets each having 5 elements and B1,B2,.........Bn are n sets each With 3 elements. Let ∪i=130Ai=∪j=1nBj=S and each element of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's , then n =
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a
15
b
3
c
45
d
50
answer is C.
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Detailed Solution
Since s=∪i=130Ai Now element in the union S belongs to exactly 10 of the A1is so n(s)=110 ( 5 x 30 ) = 15 Again s=∪j=1nBj ∴ n(s)=19(3xn)=n3 Thus n3=15 ⇒n=45