# Thread: Need formula to calculate # of unique combinations as n & m vary

1. ## Need formula to calculate # of unique combinations as n & m vary

Can anyone give me a formula to solve the following kind of problem?

Take n different colors of sand.
Using a minimum quantity m (i.e. 1%) create all the possible % combinations of the colors. {0, 0, 0, .... 100}, {100, 0, 0, 0, ... 0}, {0, 1, 0, 0, ...99}, etc.

I need a formula to calculate how many different unique combinations I would get as n and m vary.

At first I thought I could do this with

n^(m-1)

but I'm not so certain now.

Thx

2. Please clarify what you mean. I simply cannot understand what you are asking.
What do “{0, 0, 0, .... 100}, {100, 0, 0, 0, ... 0}, {0, 1, 0, 0, ...99},” repesent?
Do you have 100 colors? Or do you have 100 positions?
What does m% have to do with the count?

3. ## Clarification

I meant the sets {...} to represent all the possible combinations of the different colors of sands, given in the described case, 1% increments. The sets could also include 0% in all but 1 of the colors hence my unclear representation of {0%, 0% ,0%, ... 100%} or any other combination where the total of any given set equals 100%.

So m would equal the number (in this case) 1% intervals up to and including 100%. Other cases could have different steps or even be continuous.

So I need a formula to count all the possible combinations given n sand and m intervals.

I hope this makes it a bit clearer.

Thx.