Permutations & Combinations Calculator
nPr and nCr for any n and r, computed without factorial overflow.
Every calculation runs locally in your browser.
nPr — permutations (order matters)
720
nCr — combinations (order doesn't matter)
120
For informational and educational purposes only — not professional or technical advice, and not a substitute for consulting a qualified professional about your specific situation. TrueMeasureKit is not liable for decisions made based on these results. See our Terms of Service.
The one question that decides which formula you need
Does the order of the chosen items matter? If arranging 3 people on a podium (1st, 2nd, 3rd) counts differently depending on who's in which spot, that's a permutation — nPr. If you're just picking a 3-person committee from a group, where the same three people form the same committee regardless of the order they were chosen in, that's a combination — nCr, always smaller than or equal to nPr for the same n and r, since it collapses every reordering of a chosen set down to one count. A useful sanity check: nCr for choosing 6 numbers from 49 (a classic lottery format) works out to 13,983,816 — the actual odds quoted for that game.
Frequently asked questions
What's the difference between permutations and combinations?
Permutations (nPr) count arrangements where order matters (like ranking 1st, 2nd, 3rd place). Combinations (nCr) count selections where order doesn't matter (like picking a 3-person committee) — nCr is always smaller than or equal to nPr for the same n and r.