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.

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.