In the Mundane Goblet competition, 6 teams compete in a

"In the Mundane Goblet competition, 6 teams compete in a "round robin" format: that is, each team plays every other team exactly once. A team gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all teams (added together) in the Mundane Goblet competition?

*15
*30
*45
*60
*75
the decision:
6!/(2!*4!)=15 games
Maximum=3*15=45
Minimum=2*15=30, so
45-30=15
the correct answer is A"

Could somebody explain me please why the minimum score i had to calculate as 2*15, instead of 0*15???
I solved it as 3*15-0*15=45...or i just missed that there are no any earned scores when the team loses the game?

Why we r not taking minumun value 0??

Bunuell..what actually i was doing..i multiplied 3*15=45..

and 15*0 =0...45-15=30..

what i think because if we take 0?? then one team loss is another team win..so it will take same 45 points ...

my concept behind it is rite??

Thanks

Why we r not taking minumun value 0??

Bunuell..what actually i was doing..i multiplied 3*15=45..

and 15*0 =0...45-15=30..

what i think because if we take 0?? then one team loss is another team win..so it will take same 45 points ...

my concept behind it is rite??

Thanks

There are various ways to get a particular answer. People choose a particular method depending on how they think.

Your thought would have been something like this: There are 6 teams. The first team plays with every other team i.e. with 5 teams and goes away.
Now, the second plays with the rest of the 4 teams and goes away. Now the third team plays with the rest of the 3 teams and so on...

So total there are 5 + 4+ 3 + 2 + 1 and you used n(n-1)/2 here.

Another way to think about it is this: There are total 6 teams. Every pair of two teams played one match. Out of 6 teams, we will try to make as many distinct pairs of 2 teams each as possible. For this, we use 6C2 = 6!/2!*4!

There is absolutely nothing wrong with either one of the methods. But you must be able to think in nCr terms too because it comes in very handy in many questions. nCr = choose r items from n

For a background on combinations, check this post:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/11 ... binations/