Permutation Calculator - Calculate nPr
Calculate the number of permutations (nPr) of r items chosen from n items, with a step-by-step factorial breakdown.
nPr
336
8! ÷ (8 − 3)! = 40,320 ÷ 120
How to Calculate Permutations (nPr)
A permutation counts the number of ways to arrange r items chosen from a set of n distinct items, where order matters. It's calculated with the formula nPr = n! ÷ (n - r)!, where n! (n factorial) is the product of all positive integers up to n.
Example
How many ways can you arrange 3 out of 8 people in a line? nPr = 8! ÷ (8 − 3)! = 8! ÷ 5! = 40,320 ÷ 120 = 336. So there are 336 possible ordered arrangements.
Common Use Cases
- Counting the number of ways to award 1st, 2nd, and 3rd place among competitors.
- Solving probability and combinatorics problems in statistics coursework.
- Calculating password or PIN possibilities when digits or characters cannot repeat.
FAQs
What is the difference between permutations and combinations?
Permutations count arrangements where order matters (ABC is different from BCA), while combinations count selections where order doesn't matter (ABC and BCA are considered the same group). Since every combination of r items can be arranged in r! different orders, nPr is always r! times larger than nCr for the same n and r.
What does 0! (zero factorial) equal?
0! is defined as 1 by convention. This makes formulas like nPr work correctly even when r equals n (choosing and arranging every item), since (n − n)! = 0! = 1.
What happens if r is greater than n?
It's not possible to arrange more items than exist in the set, so nPr is undefined when r > n. This calculator shows an error message in that case instead of a numeric result.