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# number of unique triad combinations equals 528.

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number of unique triad combinations equals 528.

What is the number of unique items that makes a total of 528 unique combinations (order does not count as a combination, so ABC is the same combination as CAB)?

I found a formula for finding the number of combinations for a specified number of unique items when the number of items in a set is also specified, however that formula uses factorials and I don't know how to work around that when I don't know one of the variables.

Guest Mar 17, 2017
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I think this is basically your question:

$$528=\frac{n!}{3!(n-3)!}$$

And you're trying to solve for n.

I would just try plugging in different values for n until you find the right one.

First I tried 5, that gave me 10.

Next I tried 15, that gave me 455.

Next I tried 16, that gave me 560.

....Well...​ I don't think that n should have a fraction....I don't know, but maybe this helps some anyway.

hectictar  Mar 17, 2017