An old billionaire is writing his will, and deciding how to distribute his nine estates among his three children. He wants to give each child at least one estate, and he does not want to give any two of his children the same number of estates. In how many possible ways can he distribute his estates?

18

Step-by-step explanation:

6 2 1 How many ways does this produce and are they legitimate?

6 2 1 6 1 2 2 6 1 2 1 6 1 2 6 1 6 2

So any combination that you come up with, will produce 6 variations within those three choices. They are legitimate.

Lets see what you get with at most 5 estates to one person

5 3 1 Which will also give 6 variations. There are no other ways to make 5

4 3 2 Which will give 6 variations

I don't think there are any more possible choices.

621 531 432

Are the only 3 ways the estates can be split given the rules. Each choice leads to 6 other choices. The total is 18