Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?	Choose the correct choice from the following answers:
A) 10 B) 25 C) 126 D) 252 E) 630
With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward....   10C5 = 10!/(5!5!) = 256 possible groups of 5   Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default.   The 'twist' is that the two teams of 5 can "show up" in either order:   For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J   ABCDE vs. FGHIJ   is the SAME match-up as....   FGHIJ vs. ABCDE   So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2.   Final Answer:126
<result>C</result>
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?