Question

Eight children are divided into two teams each containing 4 children. how many different divisions are possible?

Answer 1

There are 70 different divisions possible when 8 children are divided into 2 teams, each containing 4 children.

Step-by-step explanation:

To divide 8 children into 2 teams, each containing 4 children, we can use combinations. The number of combinations can be calculated using the formula C(n, r) = n! / ((n-r)! * r!), where n is the total number of children and r is the number of children per team.

Applying this formula, we have C(8, 4) = 8! / ((8-4)! * 4!).

Simplifying this expression gives us C(8, 4) = 8! / (4! * 4!).

Calculating the factorials, we have C(8, 4) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)).

Cancelling out the common factors, we get C(8, 4) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1).

Calculating this expression, we get C(8, 4) = 70.

Therefore, there are 70 different divisions possible when 8 children are divided into 2 teams, each containing 4 children.

Answer 2

so this is what's known as a combination. a combination is a group where the order does not matter. to solve a combination, you use this equation:
n! / (r! *(n-r)!)
n is the total number of objects being sorted (8)
r is the group you need to sort them into (4)
(i know it's 2 groups of 4 but if you solve this for 1 group, the other group is automatically made of the remaining kids)
definition of !:
a number with a ! means 1*2*3...*that number (so that number multiplied by every number smaller than it all the way to one)

so we put 8 and 4 in this equation:
8! / (4! *(8-4)!)
simplify:
8! / *(4! 4!)
multiply out:
(8*7*6*5*4*3*2*1) / (4*3*2*1 * 4*3*2*1)
and put that in your calculator
you will get 70
your answer is 70