Combinations and Permutations Calculator
Free online combinations and permutations calculator. Instantly calculate nCr and nPr with or without replacement for any dataset.
Combinations & Permutations
Combinations (Order doesn't matter)
Without replacement (nCr)
120Permutations (Order matters)
Without replacement (nPr)
720Combinations
With replacement
220Permutations
With replacement
1,000What is the difference between Combinations and Permutations?
In probability and statistics, both concepts refer to the number of ways to select items from a collection. The key difference is Order.
Permutations (Order Matters)
If you are guessing a password or determining a podium finish (1st, 2nd, 3rd), the order of the items matters. Selecting A-B-C is considered completely different from C-B-A.
Combinations (Order Does NOT Matter)
If you are forming a committee or drawing a hand of cards, the order in which you pick the members or cards doesn't change the final group. A-B-C is the exact same combination as C-B-A.
With Replacement vs Without Replacement
- Without replacement: Once an item is chosen, it cannot be chosen again (e.g., drawing lottery balls).
- With replacement: An item can be chosen multiple times (e.g., rolling a dice multiple times).