jmc

Question

How many non-empty subsets of 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 consist entirely of prime numbers? (We form a subset of the group of numbers by choosing some number of them, without regard to order. So, 1,2,3 is the same as 3,1,2.)

Accepted Answer

We consider the subset 2, 3, 5, 7, 11 which consists only of the prime integers in the original set. Any subset consisting entirely of prime numbers must be a subset of this particular subset. And, there are 2^5 - 1 = 31 non-empty subsets of this 5-element set, which we can easily see by making the choice of including or not including each element.