Question

If A={1,2,3,4,5,6} ,then how many subsets of A contains the elements 2,3,5??

Answer 1

Step-by-step explanation:

I will assume that you want sets with distinct elements (the set {1,1} isn’t allowed for example) and you don’t care about order ( {1,2} and {2,1} are the same).

Once you have picked an element from the 6, you still have 5 elements to pick from. So that is 5 * 6 subsets. These subsets are redundant since they contain both {1,2} and {2,1}. To fix this, divide by 2.

You get 5∗62=15 subsets.

For a set of n elements, the answer is n(n−1)2 .

This number can also be computed using the Binomial coefficient. It is in fact (n2)=n!(n−2)!2!=n(n−1)2 .

I hope this was useful.