# Combinatorics Issue without repetitive combinations

We have 26 Boxes Labeled: Box 1, Box 2, Box 3 and so on. The boxes are in a specific order. We also have 15 rocks. Rocks are all identical. meaning Rock 1 is no different then Rock 2, or does not have a label. All Values the same.

Number of ways to arrange 15 rocks in 26 boxes without repitition...... Iam trying to figure out how many unique combinations we have if we put all the rocks in the boxes. We can put all the rocks in one box or of course we can spread the rocks out.

Our conclusion is using Stars and Bars - Theorem #2 by William Feller.

Iam trying to see if this is correct.

$$\binom{n+k-1}{k}$$

n = 26, k = 15

we got an answer of 40,225,345,056.

I plugged in n = 40, r = 15.

Let me know what you think.

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$40,225,345,056$ is the correct number though using stars and bars it might be easier to see as ${26-1+15 \choose 26-1} = {40 \choose 25}$ –  Henry Jun 3 '12 at 20:45