Question 1109837: 10 players have a tournament. They play 2v2 games. How many different games can be played? apparently 10 choose 4 = 210 is not correct
Answer by greenestamps(13216)   (Show Source):
You can put this solution on YOUR website!
I always find it aggravatingly easy to find what seems like a right answer to a probability problem only to find out the answer is something different. So I always like to see if I can find answers by two different methods and find that they are the same; then I have some confidence that I have the right answer.
The problem with your answer of 10C4 is that, having chosen 4 of the 10 players, there are different ways the 4 can be paired into two teams. In fact there are 3 different ways: A can be with either B, C, or D.
So using your method with this further calculation, the answer is
(10C4)*3 = 210*3 = 630.
Another way to get the same answer is as follows:
(1) 10C2 ways to choose the first pair
(2) 8C2 ways to choose the second pair
(3) 2 different orders in which those two pairs could have been chosen
The answer by this method is
(10C2)*(8C2)/2 = 45*28/2 = 630.
That gives me some confidence that this is the right answer.
Now I will watch and see if someone with more experience with probability shows us that the answer is something different....
|
|
|
