Question

Given that B= {1,2,3,4}, how many subsets have exactly two elements?

Answer 1

Let's look at a set B = {1, 2, 3, 4}.

There is one subset with no elements { } or ø.
There are 4 subsets with 1 element: {1}, {2}. {3}, {4}
There are 6 subsets with 2 elements: {1, 2}, {2, 3}, {3, 4}, {1, 3} ,{2, 4}, {1, 4}
There are 4 subsets with 3 elements: {1, 2, 3}, {1, 3, 4}, {2, 3, 4}, {1, 2, 4}
There is one subset with 4 elements, B.

There are 16 subsets in all.

The rule is a set with n elements has 2^n subset. hope this helps :)