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
Tips to related online calculators
See also our combinations with repetition calculator.
Would you like to compute count of combinations?
Would you like to compute count of combinations?
You need to know the following knowledge to solve this word math problem:
Related math problems and questions:
- Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace, and 2 in the third? - Salami
We have six kinds of salami that have ten pieces and one kind of salami that has 4 pieces. How many ways can we choose five pieces of salami in a distinct way? - Two groups
The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done? - STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled. - Combinations 6
6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap, and 1 strap. How many are possible combinations? - Defective 22153
There are 11 products in the box, of which just four are defective. How many ways can we choose five products so that at least four are not faulty? - Candy
How many ways can divide 10 identical candies to 5 children? - Beads
How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread? - Phone numbers
How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - Word OPTICAL
Find the number of possible different arrangements of the letters of the word OPTICAL such that the vowels would always be together. - Honored students
Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them? - Six attractions
How many opportunities do you have if you want to complete ten rides on the fair, but there are only six attractions? - 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 5 ques - Divisibility
Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero) - Cinema
How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners? - School group
There are 5 girls and 7 boys in the group. They sit in a row next to each other. How many options if no two girls sit next to each other. - Digits
How many odd four-digit numbers can we create from digits: 0, 3, 5, 6, 7? (a) the figures may be repeated (b) the digits may not be repeated
