Let A be a set with m elements and A1 A a subset with n elem

Let A be a set with m elements and A1 A a subset with n elements, n m.
How many subsets A2 A are there such that |A2 A1| = 3?
Provide a proof.

Solution

Given:A is set with m elements

   and A1\\subseteq A i,e A1 have n elements

   conditions are:n m and |A2 A1|=3

so that i want to take m=4,n=3

then subsets A2 A is 3!=6

minimum A2 A is 3!=6 subsets are in as condition.