Combination and Permutation Calculator

Combinations and permutations are counting techniques that answer a deceptively simple question: how many ways can you choose or arrange items from a set? The difference between them comes down to whether order matters. Permutations count arrangements where order is significant (like ranking contestants), while combinations count selections where order does not matter (like choosing team members). This calculator handles both, showing you the formula, the factorial expansion, and the final result.

Enter the total number of items (n) and the number you are choosing (r), and the tool computes both nPr (permutations) and nCr (combinations) with a complete step-by-step breakdown. It expands the factorials, cancels common terms, and shows the arithmetic clearly so you can follow the logic and learn the process. This is especially helpful for students preparing for exams in statistics, discrete math, or probability.

Beyond academic exercises, these calculations appear in real-world scenarios more often than you might expect. Lottery odds, password complexity, sports brackets, committee formation, DNA sequence analysis, poker hand probabilities, and experimental design all rely on combinatorics. This tool gives you quick, accurate answers with the mathematical reasoning to back them up.