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}.)
+26396 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}.)
The set of prime numbers {2,3,5,7,11} consist of 5 elements.
The subsets with one element =(51)=5 subsets.
The subsets with two elements =(52)=10 subsets.
The subsets with three elements =(53)=10 subsets.
The subsets with four elements =(54)=5 subsets.
The subsets with five elements =(55)=1 subset.
The sum is 5+10+10+5+1 = 31 subsets
