# How many different combinations of 15 alphabetized letters are possible? Using each letter only once

I think the question is self explanatory, but that's usually a bad assumption. Let me know if you need clarification. Thanks.

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## 1 Answer

Do you mean, how many different sequences of 15 letters can we do if we use each letter from the alphabet (26 letters) no more than once?

That would be: $$\prod_{i=26}^{12} i$$

For the first character you have 26 possibilities, for the second 25, ..., for the 15th you have 26-14 = 12 possibilities. Since these are independent (after you choose a character you always have one less letter to pick from) you just multiply them together.

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