Counting Foundations

Permutations of Three

List all ordered arrangements of three objects. This is a small deterministic example, not solver engineering.

combinatorics-search Every row is intentionally ordered and pinned to the lesson specification.

Example

List all ordered arrangements of three objects.

highlighted = computed this step

Step 1 — Items

Set up the exact small combinatorics values.

items(A, B, C)\begin{array}{c|c}\text{items}&\text{(A, B, C)}\end{array}

Step 2 — Permutation

Compute the highlighted combinatorics value.

permutation(A, B, C)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(A, B, C)}}\end{array}

Step 3 — Permutation

Compute the highlighted combinatorics value.

permutation(A, C, B)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(A, C, B)}}\end{array}

Step 4 — Permutation

Compute the highlighted combinatorics value.

permutation(B, A, C)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(B, A, C)}}\end{array}

Step 5 — Permutation

Compute the highlighted combinatorics value.

permutation(B, C, A)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(B, C, A)}}\end{array}

Step 6 — Permutation

Compute the highlighted combinatorics value.

permutation(C, A, B)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(C, A, B)}}\end{array}

Step 7 — Permutation

Compute the highlighted combinatorics value.

permutation(C, B, A)\begin{array}{c|c}\text{permutation}&\hlmath{\text{(C, B, A)}}\end{array}