"A football team consists of 20 offensive and 20 defensive players. The players are to be paired in groups of 2 for the purpose of determining roommates. If the pairing is done at random what is the probability that there are no offensive-defensive pairings?"

My first thoughts were that there are (40Cr2)=720 possible pairings although i'm told its much larger than this...

Any ideas? Any prods in the right direction would be much appreciated.