Question

Let U_{i = 1} X_i for i ∈ 50 = U_{i = 1} for i ∈ n Y_i = T, where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i 's and exactly 6 of sets Y_i 's, then n is equal to :

(1) 45 

(2) 15 

(3) 50 

(4) 30

Answer 1

(4) 30

n(X_i) = 10. U_{i = 1} X_i for i ∈ 50 = T,

n (T) = 500 each element of T belongs to exactly 20 elements of 

X_i = 500/20 = 25 distinct elements 

So 5n/6 = 25 

n = 30