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Number of non-empty subsets of {1,2,3,.....

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

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The correct Answer is:
1365
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`
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