Permutation Calculator (nPr)
Permutation Calculator (nPr)
Enter the total number of items (n) and how many you're arranging (r). This calculates the number of permutations — the count of distinct ordered arrangements of r items picked from n, where order matters.
Permutations apply whenever the sequence itself matters, not just which items are chosen: ranking the top 3 finishers out of a field of racers, assigning distinct job roles to a shortlist of candidates, or counting possible arrangements for a PIN code. Because arranging {A, B, C} counts as a different permutation than {C, B, A}, the permutation count for a given n and r is always larger than (or equal to) the combination count for the same numbers — the combination calculator is the one to use instead if order genuinely doesn't matter for your situation.
- Formula: nPr = n! ÷ (n − r)! — the number of ordered sequences of length r from a set of n.
- Order matters: arranging {A, B, C} is a different permutation than {C, B, A} — unlike combinations, which treat these as the same.
- Common uses: ranking race finishers, assigning distinct roles, password/PIN arrangement counts.
How is a permutation different from a combination?
Permutations count every distinct ordering separately (1st, 2nd, 3rd place), while combinations group all orderings of the same items together as one — permutations are always larger or equal for the same n and r.
What if r is larger than n?
There are zero ways to arrange more items than exist, so the result is 0 whenever r > n.
Permutation Calculator (nPr)
Enter the total number of items (n) and how many you're arranging (r). This calculates the number of permutations — the count of distinct ordered arrangements of r items picked from n, where order matters.
Permutations apply whenever the sequence itself matters, not just which items are chosen: ranking the top 3 finishers out of a field of racers, assigning distinct job roles to a shortlist of candidates, or counting possible arrangements for a PIN code. Because arranging {A, B, C} counts as a different permutation than {C, B, A}, the permutation count for a given n and r is always larger than (or equal to) the combination count for the same numbers — the combination calculator is the one to use instead if order genuinely doesn't matter for your situation.
- Formula: nPr = n! ÷ (n − r)! — the number of ordered sequences of length r from a set of n.
- Order matters: arranging {A, B, C} is a different permutation than {C, B, A} — unlike combinations, which treat these as the same.
- Common uses: ranking race finishers, assigning distinct roles, password/PIN arrangement counts.
How is a permutation different from a combination?
Permutations count every distinct ordering separately (1st, 2nd, 3rd place), while combinations group all orderings of the same items together as one — permutations are always larger or equal for the same n and r.
What if r is larger than n?
There are zero ways to arrange more items than exist, so the result is 0 whenever r > n.