Permutations & Combinations
Local ProcessingCalculate unordered combinations nCr = n! / (r! × (n - r)!) of selecting r items from n.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
Example: Total Items (n) = 5, Selected Items (r) = 2 → 10
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Solves counting problems with four formulas. Even very large results are shown as exact, unrounded integers.
What You Can Do
- Combination nCr
- Ways to choose r of n when order does not matter, like lottery numbers.
- Permutation nPr
- Ways to choose and arrange r of n, like 1st, 2nd and 3rd place.
- With repetition nHr
- Ways to choose r when the same item can be picked more than once.
- Multiset permutation
- Arrangements of items with repeats, like "AABBC". Enter the count of each kind.
How to Use Permutations & Combinations
- 1Choose a calculationIf order matters it is a permutation, otherwise a combination.
- 2Enter n and rFor a multiset, enter the counts per kind like "2, 2, 1".
- 3Read the resultLarge results copy exactly, down to the last digit.
Examples
Common Use Cases
- The denominator of lottery or draw odds
- Counting rankings or presentation orders
- Checking probability and statistics homework
Frequently Asked Questions (FAQ)
How do I tell combinations from permutations?
If reordering the chosen items counts as the same outcome, it is a combination; otherwise a permutation. Picking 3 delegates is a combination; picking a president, vice president and treasurer is a permutation.
What if r is larger than n?
For combinations and permutations r must be from 0 to n. Combinations with repetition allow r larger than n.