Hi everyone, I know this post is more about math than Dota but I can’t get this out of my head. I know invoker has total of 10 skills. In my head I’m thinking he has 9 different choices to pick 3 out of. So 9C3, but obviously thats wrong. What’s the right math to calculate this problem?
You are creating a multiset of size 3 of the 3 orbs. (multiset just means the same element can be picked multiple times, and the order still doesn’t matter like regular sets.)
The number of multisets of size k from n options is given by the formula ((n,k)) “n multichoose k”. As other commenters have pointed out, using the stars and bars argument this is equivalent to (n+k-1,k) “n+k-1 choose k”.
So ((3,3)) = (5,3) = 5!/(3!2!) = 10.