Help with Permutations

Hi all,

I'm not mathematically fantastic so I hope this makes sense.

I've written an algorithm to generate all permutations of words from a
given alphabet.

Alphabet:

"abc"

Gives permutations:

a, b, c, ab, ac, ba, bc, ca, cb, abc, acb, bac, bca, cab, cba

In order to keep track of the progress through the algorithm, I need to
be able to calculate the total number of permutations in advance. I can
do this using the following formula:

Number of permutations of size k taken from n objects is:

n!
n_P_k = --------
(n - k)!

So I can calculate the total number of permutations off all lengths as:

P = (3! / (3! - 1!)) + (3! / (3! - 2!)) + (3! / (3! - 3!)) = 15

However, the algorithm is designed to eliminate repeated permutations
that arise as a result of having repeated letters:

Alphabet:

"acc"

Gives permutations:

a, c, ac, ca, cc, acc, cac, cca

This means that the formula above no longer works. I'm wondering if
someone can provide a formula to calculate the total of number of
permutations of *all* lengths that will be outputted in the following
scenarios:

"abc" (should = 15)

"accd" (should = 34)

"acccdde" (uncertain as to what the result should be)

I have also designed the algorithm to allow me to output only the
permutations between a minimum and maximum length. Therefore as an
extension to the formula, I would like to be able to plug in minimum
and maximum length values so that I can still correctly calculate the
number of permutations that will be generated.

I greatly appreciate your input on this matter.

.

Relevant Pages

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  • Re: Help with Permutations
    ... >>>In order to keep track of the progress through the algorithm, ... >>>be able to calculate the total number of permutations in advance. ... >> gives 1265, as quasi reported. ... either Maple has a bug or there's a bug in my program. ...
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  • Re: Permuatations [was: Please Help!!Daughter...]
    ... mathematical purity of exchanging elements. ... ", and then unifies them into a framework based on exchanges), ... It isn't that I don't know how to generate permutations. ... generate-and-discard algorithm with a bit of early pruning). ...
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  • Re: Help with Permutations
    ... >>given alphabet. ... >>Gives permutations: ... >>In order to keep track of the progress through the algorithm, ... I have calculated your sum and I get 4952 or 5023 depending on if the one ...
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    ... or is it not a general algorithm. ... Today you assert that the algorithm becomes 'general' when it applies to ... An algorithm that is totally specific to a single context ... permutations. ...
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