Improved draft lottery probability calculation

In my previous blog post about the 3-2-1 lottery, I wrote about how the probabilities for each pick change depending on how many teams trigger the top-1/top-5 constraints:

[The probabilities] depend on how many teams in the lottery have constraints on winning the #1 or a top 5 pick, and whether those teams have 1, 2, or 3 chances. In theory I could find every possible scenario and precompute them all, but that's a lot of scenarios! (Homework assignment for you: how many possible scenarios is it, exactly?)

See that little combinatorics puzzle at the end? Well only one person messaged me with an answer, wiigeneral from Discord. And after correcting a small mistake, he got it right: there are 491 scenarios.

Then we talked a little more about the challenge of generating these full tables of lottery probability odds:

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