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:

n =  84

Step-by-step explanation:

C6(9)=(69)=6!(96)!9!=321987=84  n=(69)=84

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Showing 2 comments:
The answer should be ((6,4))=(9,4)=126

29 days ago  1 Like
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:
| - 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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