How many possible team combinations are there?
I was just wondering out of curiosity, how many possible team combinations are there at the moment?
E.G 
which is 1
8 Comments
It's time to put my higher education to work. Here's how the math breaks down:
There are currently 128 champions in League, there are 5 spots to a team, and each champion can theoretically fill every role to varying degrees of success.
For the sake of simplicity, let's say that there are 5 roles, 5 slots, and 5 champions. There are two ways to answer your question; using a permutation or a combination. If we count, say, ap mid Ezreal as being different from AD Carry Ezreal, then that means we're working with a permutation, and our formula is n!/(n-k)!, where n is our champion total (128) and k is the number of roles available on a given team (5).
Going by that, we get 128!/5!(128-5)!, which is equal to 31,747,968,000. There close to 32.748 BILLION possible team comps.
However, if you don't care what a champion's role is in a given team comp, then we're working with a combination, and we have to use n!/r!(n-r)!, where, where our variables are the same, but we input for r instead of k.
If we go with that option, then the answer is 128!/213!, or 264,566,400. There are over 264 million team comps made up of unique champions.
TLDR:
31,747,968,000 team comps if you care about exact roles and 264,566,400 if you dont.
Thousands ... ?
31,747,968,000
Edit: This is for possible, not optimal.
(128x127x126x125x124 for number of available champs in each slot)