The 6 fourth-grade classes at Marathon Elementary School are having a kick-ball tournament. Each class must play each other one in the tournament. How many kick-ball games must be scheduled?
6x6=36 games
There will be (6x5)/2 or 15 games
(class A cannot play against classA, as would be the case in lisa's answer.
I also divided by 2 since class B vs class C is the same game as class C vs class B etc)
To determine the number of kick-ball games that must be scheduled for the 6 fourth-grade classes at Marathon Elementary School, we can use a combination formula.
Since each class must play against every other class exactly once, we need to find the number of combinations of 6 classes taken 2 at a time (since a game involves 2 classes).
The formula for combinations is:
nCr = n! / (r! * (n-r)!)
where n is the total number of items to choose from, and r is the number of items being chosen.
In this case, we have 6 classes (n = 6) and we want to choose 2 classes for each game (r = 2).
Plugging the values into the formula, we get:
6C2 = 6! / (2! * (6-2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / 2!
Calculating further:
= (6 * 5) / (2 * 1)
= 30 / 2
= 15
Therefore, there must be 15 kick-ball games scheduled for the tournament.
To determine the number of kick-ball games that need to be scheduled for the tournament, you need to calculate the number of possible matchups between the six fourth-grade classes.
Since each class needs to play against every other class exactly once, you can use the combination formula. The formula for calculating combinations is C(n,r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items selected at a time without repetition.
In this case, n (the total number of classes) is 6, and r (the number of classes chosen at a time) is 2 (since each game involves two classes). Therefore, the formula can be written as C(6,2) = 6! / (2!(6-2)!) = (6*5*4*3*2*1) / ((2*1)(4*3*2*1)) = 15.
Hence, there need to be 15 kick-ball games scheduled for the tournament.