# Summary: Permutation Arrangement Combination

Combinatorics cheat sheet - 05/2023 - #Jumble

**There are 3 ways to make a**

__disposition__of objects:__Mnemonic:__3d

**PaC**

**P**ermutation

**a**rrangement

**C**ombination

**Ordered =>****"Permutation"****Every object:**any possible ordered disposition of \(n\) objects.- With repetition \(n^n\)
- No repetition \(n!\)
**Subset of objects:****"Arrangement**" a disposition of \(k\) objects from a set of \(n\) objects.- With repetition \(n^k\)
- No repetition \(P^n_k=\frac{n!}{ (n-k)!} = \binom{n}{k} \ . \ !k\)
**Unordered => "**Combination"

Bag of stuff: pick \(k\) elements from \(n\) bins/objects.- With repetitions \(\binom{n+k-1}{k}\)
- No repetitions \(C^n_k =\binom{n}{k}\)

__Note:__Arrangement are often viewed as a sub-set of Permutations.

Other kind of dispositions:

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