Really it was a beautiful explanation, covering all the cases fluently and in a much simpler and easier way. The mathematical part of the number of ways is explained beautifully.
no itβs not,basically for a correct pairing if all the four members are sorted and after sorting the order is [A,B,C,D] then A,B should be in first team and C,D should be in second team,in case of equal values we can swap equal members resulting in multiple team formation for your case [1,1] and [2,2] is the valid team partition
really loved the new concept used in the problem