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I need to know the total possible unique variations there can be on an identifier that is made up of 20 alphanumeric characters, where the characters are A to Z (all upper case), and the digits 0 to 9.

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    What do you mean by 'variations' and 'identifier' here? Are you looking for the number of ways that you can form a string of $20$ characters from A-Z and 0-9?2012-09-27
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    Yes. I am referring to the 'LEI' or "legal entity identifier' that all hedge funds must start using. It consist of the letters A through Z and the numbers 0 to 9. I was wondering on how many permutations there are. It looks like I already have my answer, thanks to all!2012-09-27
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    Does anybody know what number this would be i.e. million, billion, trillion etc?2012-09-27
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    13.36 nonillion2012-09-27

2 Answers 2

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If by this question you mean the number of strings of length $20$ from the alphabet $\{ A, B, \cdots, Z, 0, 1, \cdots, 9 \}$, then: there are $36$ letters in this alphabet, and you can choose any one of them for each of the $20$ characters in the string, so that leaves $36^{20}$ possible strings.

That's a lot of strings. $13\,367\,494\,538\,843\,734\,067\,838\,845\,976\,576$ to be more precise.

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    Approximately $1.33675\times 10^{31}$ ways, in fact!2012-09-27
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    @BrianMScott: Or even $13367494538843734067838845976576$ ;) Wolfram Alpha has its uses...2012-09-27
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Actually, it is higher: $13,749,422,954,239,300,000,000,000,000,000$. As you have UP TO $20$ characters, you need to take into account all the possibilities prior to the max, i.e. $$36 \\ 1,296 \\ 46,656 \\ 1,679,616 \\ 60,466,176 \\ 2,176,782,336 \\ 78,364,164,096 \\ 2,821,109,907,456 \\ 101,559,956,668,416 \\ 3,656,158,440,062,980 \\ 131,621,703,842,267,000 \\ 4,738,381,338,321,620,000 \\ 170,581,728,179,578,000,000 \\ 6,140,942,214,464,820,000,000 \\ 221,073,919,720,733,000,000,000 \\ 7,958,661,109,946,400,000,000,000 \\ 286,511,799,958,070,000,000,000,000 \\ 10,314,424,798,490,500,000,000,000,000 \\ 371,319,292,745,659,000,000,000,000,000 \\ 13,367,494,538,843,700,000,000,000,000,000$$

Total sum: $13,749,422,954,239,300,000,000,000,000,000$.

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    Question explicitly asks for "20 character" alphanumeric strings, not "at most 20 character" alphanumeric strings.2015-08-28
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    @ArthurFischer: In fact, the OP asks for "the total possible unique variations there can be on an identifier that is made *up of 20* alphanumeric characters". Yes, this is poor English, but Eva's interpretation is correct. Could you please reconsider your vote?2015-08-28
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    @AlexM. "...that **is made up of** 20 alphanumeric characters...." _Be made up of_: be composed of, be constituted of, consist in, consist of.2015-08-28
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    @ArthurFischer: Haha, my mistake. I had misinterpreted it as a mistaken version of "*made of up to 20* alphanumeric characters".2015-08-28