# Indistinguishable 64624

The father has six sons and ten identical, indistinguishable balls. How many ways can he give the balls to his sons if everyone gets at least one?

### Correct answer:

**Showing 2 comments:**

**Dr Math**

For this problem, we can just assume that everyone gets one immediately, giving us 4 available balls with six sons. Now, to visualize how we can distribute the 4 balls to 6 sons, we can just do this:

0-ball

| - separator

Some example configurations:

0000||||| - means there are 4 balls (+1 additional) for the first son, and none for the other ones

000|0|||| - means there are 3 balls for the first son, 1 ball for the second son, and none for the other ones

So the only question we need to know is how many ways can we arrange 0000|||||? The answer is 9!/4!5! or 9C4

0-ball

| - separator

Some example configurations:

0000||||| - means there are 4 balls (+1 additional) for the first son, and none for the other ones

000|0|||| - means there are 3 balls for the first son, 1 ball for the second son, and none for the other ones

So the only question we need to know is how many ways can we arrange 0000|||||? The answer is 9!/4!5! or 9C4

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