TITLE: In how many ways can 3 distinct teams of 11 players be formed with 33 men?
QUESTION [5 upvotes]: Problem:
In how many ways can 3 distinct  teams of 11 players be formed with 33 men?
Note: there are 33 distinct men.
The problem is similar to this one:
How many distinct football teams of 11 players can be formed with 33 men?
Fist, I thought the answer was:
$$
\binom{33}{11} \times \binom{22}{11} \times \binom{11}{11}
$$
But there are clearly a lot of solutions overlapping.

REPLY [3 votes]: And yet another approach...
Line the 33 men up, and assign the first 11 to Team A, the second 11 to Team B and the remaining 11 to Team C.
The line can be formed in $33!$ ways. But this counts as distinct the $11!$ rearrangements of the 11 men within each of the three teams.
Thus, we have $ 33! / (11!)^3 $ ways to set up the three teams.
This calculation counts as distinct having a particular group of 11 on Team A, or on Team B or on Team C.  If this is not the case (I'm not convinced!) then divide by $3!$