Calculate permutations P(n, r) — the number of ordered arrangements of r items from n. Free online nPr calculator.
The Permutation Calculator computes P(n, r), the number of ordered arrangements of r items chosen from n distinct items. Unlike combinations, permutations care about the order of selection.
Permutations answer questions like "How many 3-letter codes can be made from 26 letters without repeats?" or "In how many ways can the top 3 finishers be arranged in a race of 10 runners?"
This tool computes P(n, r) = n! / (n−r)! and compares it with the combination count so you can see how order multiplies the possibilities.
Precise measurement of this value supports better personal and professional planning, helping you make informed decisions about how to prioritize tasks and manage competing demands. Quantifying this parameter enables meaningful comparison across time periods and projects, revealing trends that inform better decisions about personal productivity and resource management.
Precise measurement of this value supports better personal and professional planning, helping you make informed decisions about how to prioritize tasks and manage competing demands.
Permutation calculations involve large factorials. This tool computes the result efficiently and compares with combinations to clarify the effect of ordering. Regular monitoring of this value helps individuals and teams detect productivity patterns and adjust workflows before small inefficiencies become entrenched and hard to correct. Having accurate figures readily available simplifies project planning, deadline negotiation, and workload balancing conversations with managers, clients, and team members.
P(n, r) = n! / (n−r)! Equivalently: n × (n−1) × ... × (n−r+1) P(n, r) = C(n, r) × r!
Result: 720
P(10,3) = 10 × 9 × 8 = 720. There are 720 ordered arrangements of 3 items from 10.
Race finishes, password possibilities, seating arrangements, and tournament brackets all involve permutations. Any situation where the order of selection matters requires permutation counting.
When some items are identical, the formula becomes n! / (n₁! × n₂! × ...). The word MISSISSIPPI has 11! / (4! × 4! × 2!) = 34,650 distinct arrangements.
For arrangements in a circle (like seating at a round table), the count is (n−1)! because rotations of the same arrangement are considered identical.
Mastering this concept provides a strong foundation for advanced coursework in mathematics, statistics, and related quantitative disciplines.
A permutation is an ordered arrangement of items. ABC, ACB, BAC are three different permutations of the same three letters.
Permutations consider order (ABC ≠ CBA). Combinations do not (ABC = CBA). P(n,r) is always ≥ C(n,r), with equality only when r ≤ 1.
When items can repeat, the count is nʳ (n to the power of r). A 4-digit PIN from digits 0-9 has 10⁴ = 10,000 possibilities.
A derangement is a permutation where no element appears in its original position. The number of derangements of n items is approximately n!/e.
Encryption algorithms use permutations to shuffle data. The security of many ciphers depends on the infeasibility of testing all possible permutations.
Yes, P(n, 0) = 1. There is exactly one way to arrange zero items: the empty arrangement.