# Thread: number of games - counting

1. ## number of games - counting

Bball tournament, 8 teams play eachother once
What's the number of games in tournament?

Aside from making a list counting out the possibilities,
How can you quickly figure this out, and what is the reasoning behind it?

I figured
(8 teams) *(7 "each team can play this # teams" )* (1 game/2 teams)
so 28 is answer, which is the same i get when making a list of all the possibilities by hand.

but am not sure what 7 exactly refers to--
Looks like the number of other teams each team could play against.
What would you describe it as? (what it is called doesnt seem to "cancel out" here--but what is it called anyways)

PLease let me know what you think !! thanx

2. Eight teams playing two at a time:
$\displaystyle {8 \choose 2}=\frac {8!} {(2!)(6!)}=\frac {(8)(7)}{2}$

Originally Posted by Plato
Eight teams playing two at a time:
$\displaystyle {8 \choose 2}=\frac {8!} {(2!)(6!)}=\frac {(8)(7)}{2}$

what is (8/2) ?
Is this Combination problem?
where you say number of larger group n=8, number choosing "choose 2 " k=2?

n!/(k!(n-k)!)

But this is weird because you wouldn't think that it would be "choose 2"
8 teams, choose 2? that's weird. or is it ,choose any 2 to play eachother

How many different ways to chose 2 teams from 8 players!!!
Got it!
Or Number of different games of 2 teams that can be selected from 8 teams?