@thoughtfulmongoose
I think the reason for this is because when you take the smaller one from each line (62 to 25) and add the remaining (24-1) the subset becomes {1,2,...62}, hence the 62.
Not really 🙂 Notice how Elmo has three blocks. It wouldn't be $$\binom{9}{3}$$ because you use a separate block every time so you would have to choose the first block, then the second, and so on. Try to see where you can go from there 😉
Note: Sorry this is so late I doubt you're active on this forum anymore.
@Bella Nice! 😄 That's definitely a valid way of doing it-- splitting into cases based on whether the triangles are equilateral, isosceles, or scalene (no two sides with the same lengths) is a good choice, because then it makes it harder to accidentally miss a triangle. Just goes to show that there are often multiple ways to solve a problem!
