Question

Suppose A₁, A_2,..., A₃₀ are thirty sets each having 5 elements and B_1, B₂,...B_n,..., are n sets each having 3 elements. Let

= S   

and each elements of S belongs to exactly 10 of Ai ’s and exactly 9 of Bj ’s. The value of n is equal to 

(a) 15                  (b) 3 

(c) 45                  (d) None of these

Answer 1

Correct option is (c)

Explanation:

If elements are not repeated, then number of elements in A₁ ∪ A₂ ∪... ∪ A_n ... is 30 x 5. But each element is used 10 times so, S = (30 × 5)/10 =15. Similarly, if elements in B₁,B₂,...,B_n are not repeated, then total number of elements is 3n but each element is repeated 9 times so, 

S = 3n/9 = 15 ⇒ n = 45.