What is the probability that?

For those who like maths out there, can you help me verify my calculations please?

So I was playing League of Legends and one mode of play is 5 players against 5 players.

Now, each team cannot have duplicates, and may chose a champion from a population of 123 champions.

The two different teams however can have duplicates. So for example both teams my choose exactly the same 5 champions.

The question is... What is the probability that the 2 teams choose the same combination of champions? i. e Team A has the same 5 champions as team B.

I calculated that it is 1 in 216,071,394.

Do you agree with my calculations?


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Most Helpful Guy

  • Before I do the math, let me get this straight... so each team chooses 5 champions from among 123... and you are asking what are the odds that two teams choose exactly the same five, assuming the choices are completely random? Which they wouldn't be if there is some criteria for choosing, but lets ignore that for now...

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    • So 5!118!/123... yes I would agree with your figure if the assumptions are as I stated.

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    • I have a degree in Math. Work with computer software now.

    • Oh man WOW that is so cool. I respect maths, and I think Mathematicians are the most lucid, clear thinking and clever people out there. :)

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