Permutation & Combination Calculator
Free online combinatorics calculator. Easily compute permutations (nPr) and combinations (nCr) to determine absolute probabilities without complex factorial math.
Combinatorics: Order Matters
When selecting a subset of items from a larger pool, determining whether your selection order matters drastically changes the total number of mathematical possibilities.
- Permutations (nPr): Use permutations when the sequence of selection matters (e.g., choosing a 1st, 2nd, and 3rd place winner in a race). The formula naturally produces a much larger number.
- Combinations (nCr): Use combinations when the absolute order does not matter (e.g., drawing five random cards from a standard deck).
Frequently Asked Questions
What is the mathematical difference between nPr and nCr?
A permutation (nPr) accounts for strict ordering, while a combination (nCr) simply calculates the sheer number of distinct groups you can create, regardless of internal sorting.
Why do combinations yield smaller results than permutations?
Because combinations treat different ordering of the same items as the exact same group, drastically reducing the total number of unique possibilities compared to permutations.
Ad Space - horizontal