Mark the correct alternative in the following:
Suppose A₁, A₂,...,A₃₀ are thirty sets each having 5 elements and B₁, B₂,...,B_n are n sets each with 3 elements, let and each element of S belongs to exactly 10 of the and exactly 9 of the , then n is equal to

Question

Philoid · Accepted Answer

If elements are not repeated then number of elements in A₁⋃A₂⋃A₃⋃….⋃A₃₀=30*5=150

But, each element of S is in 10 of

If elements are not repeated then number of elements in B₁⋃B₂⋃B₃⋃….⋃B_n=3*n

But, each element of S is in of

∴3× n=15× 9

∴n=45

Mark the correct alternative in the following:Suppose A1, A2,...,A30 are thirty sets each having 5 elements and B1, B2,...,Bn are n sets each with 3 elements, let and each element of S belongs to exactly 10 of the and exactly 9 of the , then n is equal to