This is also me. I was a double CS and Math major in university and one of my favorite classes as a young lad was combinatorics and probability.. 25 years ago..

It's true, if you don't activate this area of your brain often, it's easier to brute force the solution and reach for the easy mechanical calculation. I can feel this when I'm refactoring code. Today, I just have Claude do it for me with a few instructions. Each day, I feel a tiny bit more ignorant about the actual framework's APIs, its abstractions, and its rules. But I still would rather do other things with my time.

As for the problem, luckily for me, this one was easy to derive if you remember factorials, permutations, and remember to account for duplicate patterns