2015 AMC 8 Problems/Problem 13
How many subsets of two elements can be removed from the set so that the mean (average) of the remaining numbers is 6?
Since there will be elements after removal, and their mean is , we know their sum is . We also know that the sum of the set pre-removal is . Thus, the sum of the elements removed is . There are only subsets of elements that sum to : . Therefore, our answer is .