Determine number of possible combinations.

[btbam91]

Hello everybody. I have a simple combination problem.

If I am trying to generalize the number of possible combinations of a nxn block with n objects.

So let's say we have n=5.

If we have a 5x5 block (25 spaces) with 5 objects (assume objects cannot share spaces), what is the total number of combinations possible?

My first guess was 5^3 = 125, but that doesn't seem likely. I then played with the idea of holding one object static and trying to count the number of combinations of all the other objects. That didn't work. So here I am.

Thanks ahead of time for the help.

 

[Office_Shredder]

Are the objects indistinguishable (if I flip two it counts as the same configuration)

If so, don't think of it as placing objects, think of it as picking spaces. You have 25 spaces, and you have to pick five of them to place objects. This then becomes the more general question: I have n things and I want to pick k of them, how do I do it? There's actually a function for this which is called the binomial coefficient (often read as "n choose k"). You might know it already, if not it is a good exercise to try to figure out the answer.

 

[haruspex]

... Or perhaps you mean there are 5 kinds of object (and an unlimited number of each)?

 

[phinds]

Hey, I have an idea ... btbam91, how about you tell us what you DO mean so we don't have to keep guessing?