Permutation with exception/repetition

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SUMMARY

The discussion focuses on calculating permutations of a multiset, specifically when creating 3-digit numbers from a set of 5 elements that include duplicates. The user provides examples with the sets {1, 1, 1, 2, 3} and {1, 1, 2, 2, 3}, resulting in 13 and 18 variations, respectively. The key takeaway is the need for a formula that accounts for the selection of a subset of elements from a multiset while considering the order of arrangement.

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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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