Suppose that n people are gathered for a game requiring two teams each with k players. assume 2k <= n. 1 team wear red shirts and the other team will wear blue shirts. the n-2k people not on either team will just watch. we can choose the teams in either of 2 ways. 1 choose k players to wear the red shirts then choose k others to wear blue shirts. 2 the other is to choose the 2k players and then choose k of them to be red and the other will be blue. prove via combinatorial identity that these 2 methods are the same.