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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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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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