how would I use a 'combinatoral proof' to prove this:
and here's a question that has got me puzzled..
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.
(a) If the pairing is done at random, what is the probability that there are no offensive-defensive pairs?
(b) What is the probability that there are 2i offensive-defensive roommate pairs (with i= 1,2,...,10)
Thanks in advance