Permutation with exception/repetition

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To calculate permutations with repetition from a multiset, the formula is based on the total number of elements and the frequency of each unique element. For a set of n elements where some elements repeat, the formula is n! / (n1! * n2! * ... * nk!), where n is the total number of elements, and n1, n2, ..., nk are the frequencies of the distinct elements. In the case of creating a 3-digit number from the set {1, 1, 1, 2, 3}, the calculation involves selecting 3 elements from these 5 while considering the repetitions. This approach can be complex, but it allows for the determination of unique permutations based on the chosen elements. Understanding this formula is essential for accurately calculating the number of variations possible.
Crazorin
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I need a formula to calculate permutation.
For example I have a 5 numbers and I creating a 3 digit number from it.
The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula.
If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote them up properly)
Is there a formula to calculate this, or is it becoming too complex?
 
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Crazorin said:
I need a formula to calculate permutation.
For example I have a 5 numbers and I creating a 3 digit number from it.
The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula.
If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote them up properly)
Is there a formula to calculate this, or is it becoming too complex?

You're looking for permutations of a multiset (a set in which redundant elements are allowed).
(See https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets.)
 
aikismos said:
You're looking for permutations of a multiset (a set in which redundant elements are allowed).
(See https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets.)

Thanks. It is almost what I need except in those example they use up all element of each set.
I would only use part of it. So if the sets are {1, 1}{2, 2}{3} then I have a total of 5 elements. And the question is how many different 3 digit numbers I can create of these 5 elements. Because they are numbers, the order matter so it would be a kind of permutation.
What would be the formula for that?
 

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