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How many subsets of 2 elements can be removed from the set {1,2,3,4,5,6,7,8,9,10,11} such that the mean becomes 6? 

 May 30, 2020
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Since there will be 9 elements after removal, and their mean is 6, we know their sum is 54. We also know that the sum of the set pre-removal is 66. Thus, the sum of the 2 elements removed is 66-54=12. There are only 5 subsets of 2 elements that sum to 12:

{1, 11}, {2, 10}, {3, 9}, {4, 8}, {5, 7}

So the answer is 5 subsets. Hope this helps, whymenotsmart^m^

 May 30, 2020

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