Permutation Calculator - Combination Calculator

Use our permutation calculator and combination calculator to calculate P(n,k) and C(n,k) instantly online. Learn the permutation formula and combination formula through clear step-by-step factorial calculator breakdowns for every result. This n choose k tool helps you check combinatorics problems, compare arrangements and selections, and understand probability outcomes quickly.

Calculation Result - Permutation & Combination Analysis

Enter total items and selected items then click calculate

k must satisfy 0 ≤ k ≤ n

Complete Guide to Permutation Calculator and Combination Calculator

What is Permutation and Combination?

Permutation and combination are fundamental concepts in combinatorics. A permutation focuses on arrangements where order matters, while a combination focuses on selections where order does not matter. Understanding permutation vs combination helps you decide when to use permutation and combination in probability, statistics, and real-world counting problems. The formulas are: P(n,k) = n! / (n-k)! and C(n,k) = n! / (k! × (n-k)!).

Permutation Formula and Combination Formula

The permutation formula is P(n,k) = n! / (n-k)!, which counts ordered arrangements of k items from n.

The combination formula is C(n,k) = n! / (k! × (n-k)!), which counts unordered selections of k items from n. Use a factorial calculator to simplify these calculations, and follow these formulas to learn how to calculate permutations and combinations step by step.

Real-World Applications of the Permutation Calculator and Combination Calculator

  • Probability - Use the permutation calculator and combination calculator to calculate lottery odds
  • Security - Apply the permutation formula to evaluate password strength
  • Scheduling - Use the combination formula to plan tournament matchups