Question

A soccer league has 6 teams. During one season, each team plays each of the other
teams 2 times. What is the total number of games played in the league during one
season? Should be obvious, but I'm just not getting this.

Answer 1

30

Answer 2

helps, I suppose. Not sure how you'd get that, but I'll figure it out. Thanks for the help.

Answer 3

sorry i didn't explain

lets call each of the team a letter from a to f

so
team 1 is a
team 2 is b
team 3 is c
team 4 is d
team 5 is e
team 6 is f

now to make things easier to understand lets try and work out how many times a game would have been played if they played each teem once instead of twice

it would look like this

ab
ac
ad
ae
af
bc
bd
be
bf
cd
ce
cf
de
df
ef

we also have to remember that to play a GAME you need two teams

so if you count the amount of games played you will see it is 15

but because they played each team twice we multiply the number of games by 2

giving you 30 games

now there is also a formula to work this out but the way I showed above may help you understand better

the formula is

\[x = {6 \over ((6 - 2)! * (2!))}\]

Answer 4

where 6 is the number of teams and you need two teams to play a game

Answer 5

argh i made a mistake in the formula i wish there was a edit feature let me rewrite the formula

\[x = {6! \over ((6 - 2)! * (2!))}\]

Answer 6

so the formula will now look like this

\[x = {(6 * 5 * 4 * 3 * 2 * 1) \over (4 * 3 * 2 * 1) * (2 * 1)}\]

Answer 7

that will then be

\[x = {720 \over 24 * 2}\]

Answer 8

which then equals to 15 games

but that was to work out how many games would be played if they each played each other once so just multiply the amount of games by 2 and you will have your answer which is 30

remember to click good answer :)