Q.

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
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