Four teams are playing in a tournament. Each team will play each other one more time before the top two teams play the championship game. How many games will be played?
Need some help with this mates.
combinations of four taken two at a time = 4C2 = 4!/[ 2! (4-2)! ]
= 4*3*2 /(2 * 2) = 6 games before the final
so 7
Whoops, you do not do it that way in grade 5
Make a grid
___A___B___C___D
A --- * --* --*
B----------*---*
C--------------*
D ------------- The stars are the games played in the first round
You see there are 6 of them
then the final is 7
That did not line up right, but I hope you see the point
another way
A plays the other 3
B plays only C and D more because has already played A that is 2 more
C plays only D because has played A and B so one more
3+2+1 = 6 again
plus that last game = 7
Thanks mate. I owe ye big time.
(I'm not in 5th grade ;P)
You are welcome :)
At the volleyball championship tournament 7 teams are registered.If each teams must play each of the other teams how many games will be played math question.
In analysing the words of the question the words " one more time " to me imply that these teams played each other TWICE.
Therefore the number of games played will be : 3 + 2 + 1= 6games for the first round then another 6 games return matches plus the final game making a total of 13 games.
(i.e)
2(3+2+1)+ 1(Final game )
= 2(6)+1
= 12+1
= 13 games
To determine the total number of games that will be played, we need to calculate the number of games played in each round and then sum them up.
Since there are four teams, each team will play against three other teams (excluding themselves) in the initial round robin stage.
To calculate the number of games in the round robin stage, we can use the combination formula. The formula for the number of combinations (games) that can be formed from a group of n items (teams) taken k at a time is:
C(n, k) = n! / (k!(n - k)!)
In our case, n = 4 (number of teams) and k = 2 (since each game involves two teams). So, the number of games in the round robin stage is:
C(4, 2) = 4! / (2!(4 - 2)!) = 6 games
After the round robin stage, the top two teams will play the championship game. So, there will be one additional game in the tournament.
Therefore, the total number of games will be:
Round robin stage games + Championship game = 6 games + 1 game = 7 games.
So, a total of 7 games will be played in the tournament.