How many ways can 15 people be divided into 3 classes of 5, if there are 3 blond people and each class needs to have 1 blond person?
My attempt at the question:
First, the 3 blond people are excluded from the 15, leaving us with 12. To divide the 12 people into 3 groups of 5, where each group has 1 person already, we must do: 12C4 * 8C4 * 4C4
Now, this is where I get a little confused. I think that, because the groups are "distinct", due to the presence of 1 blond person in each group, there's no need to divide by 3!, despite the groups being of equal size.
Is this logic correct?
As a spin-off question, if all the blond people have to be in 1 class, then we'll have to do 12C2 (to choose the other 3 people for that class) * 10C5 * 5C5 divided by 2!, as the other two classes aren't distinct. Is this correct?
I don't have solutions to these questions so I cannot determine if it's right or wrong. Any advice will be much appreciated.
Yes. The logic is correct.
For the first, each blonde person identifies their group.
For the second, only the group with them all is uniquely identified.