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Suppose, A(1),A(2),"……..",A(30) are thir...

Suppose, `A_(1),A_(2),"……..",A_(30)` are thirty sets each having 5 elements and `B_(1), B_(2), B_(n)` sets each with 3 elements, let `underset(i=1)overset(30)(uu) A_(i) = underset(j=1)overset(n)(uu) B_(j) =S` and each element of S belongs to exactly 10 of the `A_(i)'s` and exactly 9 of the ` B_(j)'s`. Then, n is equal to

A

15

B

3

C

45

D

35

Text Solution

Verified by Experts

The correct Answer is:
C
If elements are not repeated, the number of elements in `A_(1) uu A_(2) uu A_(3) ,"…….."uu A_(30)` is `30 xx 5`
But each element is used 10 times, so
`S = (30 xx 5)/(10) = 5`
If elements in `B_(1), B_(2)"…….",B_(n)` are not repeated, then total number of elements is 3n but each element is repeated 9 times, so
`S = (3n)/(9) rArr 15 = (3n)/(9)`
`:. n = 45`
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