This question, from a friend's homework, interested me, so I thought I'd work it out and post my result here.
Query: how many ordered triplets (a,b,c) are there such that 1≤a≤b≤c≤N? Answer: fix the low end, a, and the high end, c, and there are c-a+1 triplets in this family. This is also the length of the line between c and a on the number line,
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