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How many combinations can be using 3 alphabet letters (from A to Z)? Note that string doesn't have to be unique, it can be eg. RPP or AZZ

zarkoz
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    $26^3$ $ $ $ $ $ $ – Math1000 Jun 06 '17 at 14:09
  • @Math1000 great thank you very much :) And is it possible to calculate how many unique strings can be without repeating letters? I mean combinations like eg. XYZ and not XXZ – zarkoz Jun 06 '17 at 14:11
  • If you want to do this without repeating letters, then you will have $26$ options for the first letter, one less option for the second letter (since one letter was taken for the first letter) and one less for the third (for the same reason) and so the total number of strings in this form is $$262524$$ – Franklin Pezzuti Dyer Jun 06 '17 at 14:16

1 Answers1

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You can make three independent choices, one for each of the three letters. For each choice you have 26 options (the letters in the alphabet). So the total number of combinations is

$$ 26 \cdot 26 \cdot 26 = 26^3 = 17576. $$

If you want the letters to be unique, the calculation changes slightly. You still have 26 options for the first choice, but for the second choice there are now only 25 options available (all letters except the one you already chose), and for the third choice there are 24 options available (all letters except the two you already chose). So this gives you:

$$ 26 \cdot 25 \cdot 24 = 15600. $$

JSQuareD
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