Counting Principles: 15 Ways Explained

[Seneka]

Homework Statement

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

Relevant Equations

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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.]

 

[symbolipoint]

I'm not an expert on combinatorics or counting-principles, but the problem seems not sufficiently described.

 

[Seneka]

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.

 

[jedishrfu]

It seems its missing the 4 distinguishable toys part. Maybe one toy was a dinosaur and ate its neighbor.

https://www.quora.com/How-many-ways-can-I-organize-4-distinct-toys-into-3-different-boxes

 

[WWGD]

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?