Permutations

1. Senior Member
Join Date
Dec 1969
Posts
490

## Permutations

Hiya,<BR><BR>I&#039;ve not got a calculator in the office big enough and i can&#039;t remember the math for factorial so sadly i&#039;m here to see if i can get an answer to this quicky.<BR><BR>Can anyone tell me how many permutations there are for a 5 letter sequence using the folowing characters.<BR><BR>bcdfghjkmnpqrstvwxyz<BR><BR>Tha ts 20 factorial times 5 if i remember rightly...<BR><BR>I&#039;m basically trying to calculate how many random passwords this sequence will give me.<BR><BR>Thanks in advance,<BR><BR>Kes<BR>

2. Senior Member
Join Date
Dec 1969
Posts
10,852

## RE: Permutations

20!*5? Nah...That&#039;s way too many. <BR><BR>You have 20 choices for the first character. Then you have twenty choices for the second character....So for each of the first twenty characters that you have, you could have twenty differnt choices that could follow it. 20*20, or 400. For each of those 400 two-character sequences, you then have another 20 characters that could follow. 400*20, in other words. Follow that though, and you get 20*20*20*20*20, or 3,200,000 possible sequences. <BR><BR>The easiest way for us to see this, is to use Base10 character sets. Instead of the twenty characters that you gave, say your choices were 0123456789. Ten numerals. How many choices would you have for a two digit sequence? Well, we have ten numerals for the first charater, and each of those could be followed by any of the ten numerals, so 10*10, or a hundred choices. We also know from elememntry school that the range of two digit numbers is 00,01,02...97,98,99; One hundred possibilities. So the math works. For a three character sequence, 10*10*10 = 1000. 000-999 are the possible values...One thousand possibilites. <BR><BR>A factorial would only come into play if you weren&#039;t using replacement. If each of the characters in the sequence had to be unique. If 985 were allowable, but you didn&#039;t want 998, or 757 in other words. In that case, you&#039;d be limited to 10*9*8, or in the original case, 20*19*18*17*16 as characters are used and eliminated from the set of possible choices for following characters. (This isn&#039;t a complete factorial, of course, but is along the lines of what you were thinking.)

3. Senior Member
Join Date
Dec 1969
Posts
490

## Thats plenty...

... thanks for that.<BR><BR>Has been a while methinks

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