Probability - Gravner-15.b

Question

A tennis tournament has $2n$ participants, $n$ Swedes and n Norwegians. First, $n$ people are chosen at random from the $2n$ (with no regard to nationality) and then paired randomly with the other $n$ people. Each pair proceeds to play one match. An outcome is a set of $n$ (ordered) pairs, giving the winner and the loser in each of the $n$ matches.

(b) What do you need to assume to conclude that all outcomes are equally likely?