Answer 2: Break this problem up into cases by what the middle number in the subset is. Say each subset is \(\{a,b,c\}\) written in increasing order. We count the number of subsets for each distinct value of \(b\text{.}\) The smallest possible value of \(b\) is \(2\text{,}\) and the largest is \(n+1\text{.}\)
in-context