Problem Solving questions I dont get? combinations maybe?

[kapitalist]

Team/Number of games won

A/4
B/7
C/9
D/2
E/2
X/?

(it was a table but I cant draw it here).

Question: According to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game)

I thought this was a Combination question, but I dont understand how they got the answer?

Answer choices:
A 4
B 5
C 6
D 8
E 10

If you can explain this one for me that would be awesome.

[Brent@GMATPrepNow]

Team/Number of games won

A/4
B/7
C/9
D/2
E/2
X/?

(it was a table but I cant draw it here).

Question: According to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game)

I thought this was a Combination question, but I dont understand how they got the answer?

Answer choices:
A 4
B 5
C 6
D 8
E 10

If you can explain this one for me that would be awesome.

You're right; this is a combinations question.
First, determine the total number of games played.
Let's say that each team plays every other team exactly once. How many games will there be? Well, select two teams from the six teams and have them play each other. In how many ways can we select 2 teams from 6 teams and have them play each other? 6C2 (15) ways.
So, if each team plays every team twice, then there are 30 games in total.
If there are 30 games in total, then there are 30 wins. In other words, the number of wins in the table should add to 30.
We get 4+7+9+2+2+? = 30
The missing value is 6

[kapitalist]

[quote="Brent Hanneson"][quote="kapitalist"]Team/Number of games won

A/4
B/7
C/9
D/2
E/2
X/?

(it was a table but I cant draw it here).

Question: According to the incomplete table above, if each of the 6 teams in the league played each of the other teams exactly twice and there were no ties, how many games did team X win? (Only 2 teams play in a game)

I thought this was a Combination question, but I dont understand how they got the answer?

Answer choices:
A 4
B 5
C 6
D 8
E 10

If you can explain this one for me that would be awesome.[/quote]

You're right; this is a combinations question.
First, determine the total number of games played.
Let's say that each team plays every other team exactly once. How many games will there be? Well, select two teams from the six teams and have them play each other. In how many ways can we select 2 teams from 6 teams and have them play each other? 6C2 (15) ways.
So, if each team plays every team twice, then there are 30 games in total.
If there are 30 games in total, then there are 30 wins. In other words, the number of wins in the table should add to 30.
We get 4+7+9+2+2+? = 30
The missing value is 6[/quote]


ahhh

6!/(2!(6!-2!) = 15

15x2=30

30-24=6

I dont know how im going to crank these out on test day in under 1.5 min??

Thanks so much