Number of non-empty subsets of {1,2,3,..,12} having the property that sum of the largest and smallest element is 13.

Answer

1365

Explanation

Set must contain minimum two elements, such that sum of smallest and largest element is 13.
If set contains smallest number 1 and largest number 12 then we can select other elements of subset from {2,3,..,12}.
So, number of subsets are `2^(10)`.
If set contains smallest number 2 and largest number 11 then we can select other elements of subset from {3,4,..,10}.
So, number of subsets are `2^(8)`.
Similarly, we have subsets `2^(6),2^(4),2^(2),2^(0)`.
So, total number of subsets `1+2^(2)+2^(4)+..+2^(10)=1365`