How many subsets of {0, 1, ..., 9} have the property that there are at least two elements and the sum of the two largest elements is 10?
\(\phantom{13}\)
+128475
Elements Containing Number of subsets
9 ,1 and 1 other possible element 2 = sum of row 1 of Pascal's Triangle
8, 2 and 2 other possible elements 4 = sum of row 2
7, 3 and 3 other possible elements 8 = sum of row 3
6, 4 and 4 other possible elements 16 = sum of row 4
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30
Each set contains two specific elements and the the number of total number of subsets with these =
( 2) ^(possible number of other elements)
