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

 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 :)

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