Permutations Calculator P(n, r)
P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.
Result
Permutations
720
10! / (7)! = product of top 3 consecutive integers from 10.
- n10
- r3
- P(n, r)720
- C(n, r)P / r!120
- Ratio P/C= r!6
Step-by-step
- P(10, 3) = n × (n−1) × … × (n−r+1) = 10×9×…×8.
- = 720.
- Equivalently P = C × r! = 120 × 6 = 720.
How to use this calculator
- Enter n and r.
- Read permutations.
About this calculator
Permutations count ordered arrangements. P(n,r) = n! / (n-r)! = n × (n-1) × … × (n-r+1). For r = n: P(n,n) = n! (all orderings of n items). Used when sequence matters: race orderings, password permutations, seating arrangements. Always P(n,r) ≥ C(n,r) by factor of r!.
Frequently asked
Race finish (1st, 2nd, 3rd are different roles). Passwords (123 ≠ 321). Seating (Alice next to Bob vs. far apart).
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