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Permutation / Combination

Mani Ram
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Joined: Mar 11, 2002
Posts: 1140
I don't know whether this thread belongs to this forum but I couldn't any other forum appropriate for this discussion and so I'm posting it here.
Could somebody answer me with the formula for the following cases?
1) How many combinations are possible to create an alphanumeric string with a format XXXnnn where X is an uppercase letter (A-Z) and n is a digit (0-9)?
2) What if the format is flexible (say unlike the previous example even XnnXXn are nnXXnX are valid strings)? How many combinations are possible now?
3) What if the number of letters and digits in the resultant string is flexible. For example the string can be full of letters (XXXXXX) or of digits (nnnnnn) or anything in between?
4) How many combinations are possible if the lowercase letters are allowed (like XxXnXn)?


Mani
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Wirianto Djunaidi
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Joined: Mar 20, 2001
Posts: 210

Originally posted by Mani Ram:
I don't know whether this thread belongs to this forum but I couldn't any other forum appropriate for this discussion and so I'm posting it here.
Could somebody answer me with the formula for the following cases?
1) How many combinations are possible to create an alphanumeric string with a format XXXnnn where X is an uppercase letter (A-Z) and n is a digit (0-9)?

If you allow repeated alphanumeric: 26 x 26 x 26 x 10 x 10 x 10
If you disallow repeated alphanumeric: 26 x 25 x 24 x 10 x 9 x 8

2) What if the format is flexible (say unlike the previous example even XnnXXn are nnXXnX are valid strings)? How many combinations are possible now?

Same as above, as it has the same number of elements

3) What if the number of letters and digits in the resultant string is flexible. For example the string can be full of letters (XXXXXX) or of digits (nnnnnn) or anything in between?

For combination, you'll go for the highest probability,
so with 6 digit, you'll have 26 ^ 6 here.

4) How many combinations are possible if the lowercase letters are allowed (like XxXnXn)?

Well, if you allow both lower and uppercase than you'll have 52 possibilities instead of 26. Same rule apply as above.
Hope that helps.
Timothy Chen Allen
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Joined: Mar 16, 2003
Posts: 161
Originally posted by Wirianto Djunaidi:

) What if the number of letters and digits in the resultant string is flexible. For example the string can be full of letters (XXXXXX) or of digits (nnnnnn) or anything in between?
For combination, you'll go for the highest probability,
so with 6 digit, you'll have 26 ^ 6 here.

Be careful here. You actually have the possibility of 26 + 10 characters in each slot now, so it becomes 36 * 36 * 36 * 36 * 36 * 36.


Timothy Chen Allen
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fred rosenberger
lowercase baba
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Joined: Oct 02, 2003
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  16


2) What if the format is flexible (say unlike the previous example even XnnXXn are nnXXnX are valid strings)? How many combinations are possible now?

does order matter? i.e. is AAA111 different than 1A11AA? this is not the same as case 1, i think...


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Mani Ram
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Joined: Mar 11, 2002
Posts: 1140
Thanks for all.

Which totals to '26 x 26 x 26 x 10 x 10 x 10' elements as you said.
But, if strings like XnnXXn and nnXXnX are allowed, then the set should be bigger..isn't it?
Like A09BC2, 12DF3G will also be eligible candidates which are not present in the above list.
Originally posted by fred rosenberger:
does order matter? i.e. is AAA111 different than 1A11AA? this is not the same as case 1, i think...

Yes. AAA111 is different from 1A11AA.
[ November 05, 2003: Message edited by: Mani Ram ]
Mani Ram
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Joined: Mar 11, 2002
Posts: 1140
So, from your responses
-For a string with format XXXnnn, the possibilities are 26X26X26X10X10X10
-For a string which doesn't mandates the number of digits or letters in it (ex: 111111, FFFFFF are valid entries), the possibilities are (26+10)^6
-Replace 26 with 52 in the above equations, if lower case letters are allowed.
Still, one question remains: For flexi formats (like XnXnnX), the possibilities are ?
Deb Sadhukhan
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Joined: Nov 05, 2003
Posts: 67
flexi formats possibilities = XXXnnn format possibilities * possible flexi formats
possible flexi formats = (6!)/(3! * 3!) = 20
So my answer is: 26*26*26*10*10*10 * 20
Mani Ram
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Joined: Mar 11, 2002
Posts: 1140
Okay understood.
So, to create a string of 8 characters, with exactly 4 digits[0-9] and 4 letters[A-Z], with the following rules,
-Only UPPERCASE letters are allowed.
-Any character (letter or digit) can sit in any place.
The number of possible combinations are
(26*26*26*26*10*10*10*10) + (8! / 4! * 4!) => 319883200000
Right / Wrong?
Deb Sadhukhan
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Joined: Nov 05, 2003
Posts: 67
Yes Mani. You got it. Let me know if you need explanation of the latter part.
-Deb
 
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subject: Permutation / Combination