Counting Principles

  • Thread starter Seneka
  • Start date
  • #1
41
0

Homework Statement:

Q: State how many ways distinguishable toys can be put into three distinguishable boxes.
A: 81

Relevant Equations:

-
I thought the number of ways would be dependant upon the number of toys.

Since the number of toys isn't given I tried taking into the different ways you can order using different number of boxes.

First situation:

They can use all three boxes 3x2x1=6.

Second situation:

They can only use two boxes so 3choose2 x2= 6

Third situation:

They can only use one box so there are three ways as in you put all the toys in one box.

The sum of these different ways are 15 which isn't correct.

[Moderator's note: Moved from a technical forum and thus no template.]
 

Answers and Replies

  • #2
symbolipoint
Homework Helper
Education Advisor
Gold Member
6,062
1,131
I'm not an expert on combinatorics or counting-principles, but the problem seems not sufficiently described.
 
  • #3
41
0
I'm not an expert on combinatorics or counting-principles, but the problem seems not sufficiently described.
That's what I thought too. I just posted it to see if there was some interpretation of the question to make sense of the answer.
 
  • #5
WWGD
Science Advisor
Gold Member
2019 Award
5,360
3,357
This problem is usually called the problem of "Balls in boxes" , or the number of no negative solutions to ##x_1+x_2+...+x_n =k ##. Haven't you seen this in class?
 

Related Threads on Counting Principles

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
1
Views
3K
Replies
2
Views
2K
Replies
4
Views
2K
  • Last Post
Replies
3
Views
743
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
674
  • Last Post
Replies
8
Views
3K
Top