Sons
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
Tips for related online calculators
See also our combinations with repetition calculator.
Would you like to compute the count of combinations?
Would you like to compute the count of combinations?
You need to know the following knowledge to solve this word math problem:
Grade of the word problem:
Related math problems and questions:
- A man 10
A man gave 1/6 of his SSNIT benefits to his aged mother, 1/5 to his father, and 1/2 to his wife. If he still has 400 left, which he distributed among his four sons. Calculate a) his total SSNIT b) the amount is given to his mother c) the amount is given t
- Indistinguishable 81481
How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice.
- A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first five q
- Arithmetic 65324
Martin has an arithmetic average of 2.8 out of five history grades. If he only gets one from now, how many ones would he have to get at least so that the arithmetic mean of his history grades is less than 2?
- A father 2
A father gave 1/3 of his land to the daughter and the remainder to the son. Son donates 3/4 of his land for the playground. He built a house in half of the remaining area, and the other half was sold for rs.1 million. 1) give the son's portion as a fracti
- Originally 71464
The father originally wanted to divide the financial amount between his sons in the ratio of 7:6. However, he then split it at 6:5 (in the same order). One of the sons got angry that he should have received 120 euros more. How many euros did each son rece
- Cards
How many ways can you give away 32 playing cards to 7 player?