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InterviewSolution
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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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Answer» Correct Answer - 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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