How many subsets of {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19} contain at least one prime number?

Guest Nov 30, 2022

#1**+2 **

You can use complimentary counting, first let S = total number of possible subsets.

Let N = the number of subsets with no prime number, then the answer we are looking for is S - N.

S = 2^18 since there are 18 items.

N is any set with 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

There are a total of 10 items.

So S - N = 2^18 - 2^10

**261120 subsets**

proyaop Nov 30, 2022