Question

Twelve children are divided up into three groups, of five, four, and three children, respectively. In how many ways can this be done if the order within each group is not important?

Thank you so much!

Answer 1

Well if you divide 12 children into 5 groups you might find yourself in jail....I'm just saying

Answer 2

What you are asking is how many ways to arrange 3 different numbers. In general, if you have n items, there are n! ways to arrange them (permutations).

3! = 3*2*1

3 4 5
3 5 4
4 3 5
4 5 3
5 4 3
5 3 4

There are 3 ways to pick the first group
That leaves only 2 ways to pick the next group,
and only 1 way left to pick the 3rd group.

3*2*1 = 6 = 3!