OA is E.
Correct answer: (E)
Solution: For any particular game, we have 16 options for the first team and 15 options for the second. 16 * 15 = 240. For our arrangements, though, Team A against Team B is the same as Team B against Team A, so we have to divide by two to get rid of the duplicates. 240/2=120, or answer (E).
Alternatively, because the problem is essentially asking how many groups of 2 teams can be generated from a pool of 16 teams, we can use the combination formula: N!/([K!][N-K]!). Our N (the number of things to be combined) is 16, and our K (the number of things in each group) is 2. Using these values generates the same answer, 120.
Anytime that you are working with selecting two from any number you can figure out just through a little hard work. Each team can play every other team. So team A has 15 opponents - then team B has only 14 opponents because A has played B already. So you can just take the total number of teams - 1 (in this case 15) and add each decreasing number so 15+14+13+12+11+10...+1 = 120. Not the most elegant way but sometimes on the test you are stuck and need to do something.
Last edited by
David@VeritasPrep on Fri Dec 03, 2010 3:22 am, edited 1 time in total.
