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Suppose A1,A2, ...,A30 are thirty sets each having 5 elements and B1, B2, Bn are n sets each with 3 elements, let 3S0 i=1 Ai = nS i=1 Bj = S and each elements of S belongs to exactly 10 of the Ais and exactly 9 of the Bjs. Then, n is equal to

Suppose A1,A2, ...,A30 are thirty sets each
having 5 elements and B1, B2, Bn are n sets
each with 3 elements, let
3S0
i=1
Ai =
nS
i=1
Bj = S and
each elements of S belongs to exactly 10 of the
Ais and exactly 9 of the Bjs. Then, n is equal to

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
576-481_IMG_20200329_015021.jpg
Vikas TU
14149 Points
4 years ago
Dear student 
Since, each Ai has 5 elements, we have
sum from i=1 to 30 
n(Ai) = 5*30 = 150 
Let set S consists of k elements.
Since, each elements in S belongs to exactly 10 of Ai's
Therefore,
sum from i = 1 to 30 n(Ai) = 10k 
Hence 
10k = 150 
k = 15 
Now, since each Bj has 3 elements and each S belongs to exactly 9 of Bj's
Therefore,
n(Bj) = 9k 
3n = 9k = 9*15 
n = 45 
 

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