A permutation is a calculation of how many ways a set can be represented. This is a simple factorial of the number of the entire set.

Meaning if we had a set of values:

``````a, b, c
factorial(3) # 3!
> 6          # 3 * 2 * 1``````

However the formula changes as we get into more complex problems. Consider this example on BetterExplained.com:

``````# we have 8 contestants:
1: Alice
2: Bob
3: Charlie
4: David
5: Eve
6: Frank
7: George
8: Horatio

# How many ways can we award a 1st, 2nd and 3rd place price among eight contestants? ``````

P(n,k) = n! / (n-k)!

In the above equation n would be 8 (8 contestants) and k is 3 (three outcomes of Gold, Silver or Bronze medals.) That leaves us with 8! / 5!

This results in 336 possible permutations!

The above equation works for problems where repetition is not allowed.

## Permutations with Repetition

Looking at the password example from Pierian Data’s Udemy course, we have a problem of determining how many 4 digit license plates can be created using any of the 26 letters of the English alphabet + the numbers 0-9. That’s a total of 36 characters used in a password.

In this case we allow the permutation to take a repeating character, like 5555 or aaaa or acda. The equation is simply:

``````# n^k
n**k     # where k is the subset (4) of the population (36)
>>> 1679616``````

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