# Combinatorics of sports outcomes I am trying to figure out how many possible combinations of 6 figh

Combinatorics of sports outcomes
I am trying to figure out how many possible combinations of 6 fighters can be made out of a pool of 22 fighters. These are 1v1 fights (11 fights) so I don’t want any 2 fighters fighting each other to be in the same combination. I imagine it has to be something similar to 22 choose 6 but that wouldn’t account for the fighters against each other. Order does not matter.
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Nicolas Calhoun
Step 1
To summarize the discussion in the comments:
We are assuming that the fighters are paired (with each fighter appearing in exactly one pair).
To choose 6 of them, subject to the exclusion rule, we first must choose 6 of the 11 pairs. There are, of course, $\left(\genfrac{}{}{0}{}{11}{6}\right)$ ways to do that.
Step 2
Now we must choose 1 fighter from each of the 6 pairs we selected. There are ${2}^{6}$ ways to do that.
Combining all this, the answer is $\overline{)\left(\genfrac{}{}{0}{}{11}{6}\right)×{2}^{6}}$.