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September 9th, 2018, 10:18 PM   #1
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Total Combinations

Hi Forum,

I have 10 football matches being played on the weekend (Team 1 vs Team 2, Team 3 vs Team 4...Team 19 vs Team 20). I want to have a bet on a multi/parlay/accumulator with 4 teams in the bet. I want to work out how many combinations of 4 teams (each playing in different matches) exists (e.g. Teams 1-3-5-7 would be the first combination). I have written down as methodically as I can every combination in an Excel file and come up with 3352 total combinations. I want to confirm I have recorded all possible combinations. Does anyone know how to calculate the total number of combinations that should exist?

Thanks, Rob
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September 9th, 2018, 10:29 PM   #2
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First you pick 4 of the 10 games. This is $\dbinom{10}{4}= 210$

Then for each of those games you have 2 choices of which team to bet on.

That gets you $2^4=16$

So the total combos is $210 \cdot 16 = 3360$
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September 9th, 2018, 11:38 PM   #3
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Thanks romsek! I'm 8 combos short. Will go looking now!

Cheers, Rob
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