+0

# I need help!!!

0
213
1

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\}\$.)

Guest Sep 21, 2017
Sort:

#1
+19084
+1

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 \( = \binom{5}{1} = 5 \) subsets.
The subsets with two elements \(= \binom{5}{2} = 10\) subsets.
The subsets with three elements \(= \binom{5}{3} = 10\) subsets.
The subsets with four elements \(= \binom{5}{4} = 5\) subsets.
The subsets with five elements \(= \binom{5}{5} = 1\) subset.

The sum is 5+10+10+5+1 = 31 subsets

heureka  Sep 21, 2017

### 12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details