a football team consists of 20 offensive and 20 defensive players. the players are to be paired in grps of 2 for the purpose of determining roomates. if the pairing is done at random, what is the prob that there are no offensive-defensive roommate pairs?
the ans goes like this: the denominator of the prob is (40)!/((2^20)(20)!) and the numerator is ((20)!/((2^10)(10)!))^2.
why is there the (20)! at the bottom of the denominator and (10)! at the bottom of the numerator.
the book kinda explained that its 'cos its unordered pair, but i don't understand why have to divide by (20)! & (10)!?