The total number of team compositions in league of legends.

Ignoring the video itself I'd like to address the number he mentions and how he might've reached it. While it's similar to 136^5 (136 champion possibilities for each person) = 46525874176 you should really be more accurate with your calculations.

It can't be 136^5 because that would include possibilities of two people picking the same champion. Instead you would use 136! because that shows every possible way there is to organize 136 champions.

! is a notation (called a factorial) used in statistics where: n! = n x (n-1) x (n-2) x (n-3)... until you reach (n-a) = 1 so x! is = X times every number between x and 1. 136! = 136 x 135 x 134 x 133 ..... all the way down to 3 x 2 x 1

This is used because there are 136 possible champions to put in the first place, 135 to put in the second, 134 to put into the third, all the way until you have 2 champion to put in the 135th place, and one only one champion to put into the final place.

If you still don't understand, try taking 4 different coins out and laying them on a table (or just imagine in, lazy ass bum.) How many ways can you line up those 4 coins?

Well, you can put the quarter first, then the dime, then the nickel, then the penny. Or the penny, then the dime, then the nickel, and the quarter. Or the dime then the penny then the.... etc.

There are 4 coins you can put first, now no matter which coin it is, there are 3 coins you can choose from, no matter which coins are in the first places you will have 2 choices for the third, and one choice from the last. Written out this equation looks like 4 x 3 x 2 x 1 = 4! = 24. There are 24 ways to line up 4 coins.

But there aren't 4 champions. There are 136.

136! = 36590428819525486576897272205198933454286172951815726156123815101405189582089242773975735166401987907830880230417721361838572072126683305250473185240276110436058808776620558462614334914409164842205184000000000000000000000000000000000 = 3.6590428819525E+232 (for short)

So we know there are a lot of different ways to organize every champion in league, but this isn't the number we want.

We're looking for every possible composition of 5 champions from 136 champions.

So since we had 136 choices for the first champion, 135 for the second, 134 for the third, 133 for the fourth, 133 for the fifth, then we don't need 132,131,130, etc.

In order to do this we would divide 136! by 131!. 131! = 847158069087882051098456875815279568163352087665474498775849754305766436915303927682164623187034167333264599970492141556534816949699515865660644961729169613882287309922474300878212776434073600000000000000000000000000000000 = 8.4715806908788E+221 (for short)

So our new formula looks like: 136!/131! = 136 x 135 x 134 x 133 x 132 = 43191973440

WAIT A SECOND! That's the number from the video! So we know how it was found but there's still one step missing.

43191973440 is how many combinations there are but is counted once while is counted again. Same 5 champions but because we organized them differently they're counted again.

We can organize any 5 champions in 5! ways. 5! = 120 so we divide take 43191973440 and divide by 120.

43191973440 / 120 = 359933112 the ACTUAL number of team compositions in league. Granted this counts as a composition which is unlikely but considering we aren't calculating the number of PROPER team compositions then we would still say that 359933112 is the total number of compositions (FOR ONE TEAM) that can be made.

p.s if a good number of people enjoyed this post then ill do a follow up trying to calculate how many proper team compositions there are, meaning one top laner, jungler, mid, support, and adc/marksman. If not then i hope someone enjoyed it anyways :D