Summary: Permutation Arrangement Combination
Combinatorics cheat sheet - 05/2023 - #Jumble
There are 3 ways to make a disposition of objects:
Mnemonic: 3d PaC
Permutation arrangement Combination
- 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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