What can be a real-world example of Permutation without repetition? 
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?
 A: 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
A: Gold, Silver, Bronze.
(Medalists in some Olympic competition that cannot have ex aequo outcomes.)
A: Throwing $n$ distinguishable balls into $k$ distinct buckets?
Or Bingo/Secret Santa type games.
