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enter image description here

I know that a Permutation lock is a concrete real-world example of "permutation with repetition".

What can be a concrete real-world example of Permutation without repetition?

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  • $\begingroup$ They are not really permutations either way. They are called partial permutation for the case without repetition, just sequences for the case where repetition is allowed. $\endgroup$ Jul 25 at 15:23
  • $\begingroup$ A deck of cards shuffled in a particular way is an example of a permutation of 52 cards. The order matters when playing any card game. If there are no jokers there's no repetition. $\endgroup$
    – Robearz
    Jul 25 at 15:33
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    $\begingroup$ +1 for the nice image. $\endgroup$
    – Yorch
    Jul 25 at 17:50
  • $\begingroup$ There are still places where seats or spots are not assigned and who gets in first has more choices of seats / spots. As the next person coming in cannot choose the same seat, they have one less choice. $\endgroup$
    – Math Lover
    Jul 25 at 20:20
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When you say "permutation with repetition" , i thought the formula such as $$\frac{n!}{n_1 \times n_2 \times ... \times n_r}$$ For example , how many ways are there to arrange the letters of "MATHEMATICS" can be given an example.

I will not mess with "definitions" anymore . Hence , my example will be distributing letters into post boxes.

For example , if you write letters in "real life" , then when you go to post office , you would encounter with this case.

If you have $3$ letters and $5$ post boxes , then you would have $5 \times 5 \times 5 = 5^3$ different cases to put your letters into the boxes.

What's more, "permutation with repetiton" is used commonly in network systems in communication and computer sectors especially in trees in graph theory.

Please look at : https://www.quora.com/What-is-the-practical-real-life-use-of-permutation-and-combination

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  • $\begingroup$ Do you know how to get count of all the permutations with limited repetitions? Like count of all the variations between 0000000000 and 9999999999 with 5 repetitions in each variation? This is the question that I've asked: math.stackexchange.com/questions/4247472/… $\endgroup$
    – Eftekhari
    Sep 12 at 17:24
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Gold, Silver, Bronze.

(Medalists in some Olympic competition that cannot have ex aequo outcomes.)

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Throwing $n$ distinguishable balls into $k$ distinct buckets?

Or Bingo/Secret Santa type games.

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