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Back to Combinatorics

Permutations

An arrangement is a choice for every slot, in order. Without repetition each choice uses an item up, so the options shrink — n, then n − 1, then n − 2 — and the product is n! / (n − k)!.

Step 1 of 19

Speed

Five runners, A to E, race for gold, silver and bronze. A podium is an ordered list of three different runners: A-B-C and B-A-C are different podiums. Fill the medals one at a time.

P(5, 3) = \frac{5!}{(5 - 3)!} = \frac{5 \times 4 \times 3 \times \cancel{2 \times 1}}{\cancel{2 \times 1}} = \mathbf{60}

n (items)5k (slots)3

Arrangement number (dictionary order)— of 60Fill every slot, or slide to jump to an arrangement

All 60 arrangements, in dictionary order:

Permutations

An arrangement is a choice for every slot, in order. Without repetition each choice uses an item up, so the options shrink — n, then n − 1, then n − 2 — and the product is n! / (n − k)!.

Step 1 of 19

Speed

Five runners, A to E, race for gold, silver and bronze. A podium is an ordered list of three different runners: A-B-C and B-A-C are different podiums. Fill the medals one at a time.

P(5, 3) = \frac{5!}{(5 - 3)!} = \frac{5 \times 4 \times 3 \times \cancel{2 \times 1}}{\cancel{2 \times 1}} = \mathbf{60}

n (items)5k (slots)3

Arrangement number (dictionary order)— of 60Fill every slot, or slide to jump to an arrangement

All 60 arrangements, in dictionary order:

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Permutations

See also

Permutations

See also