# Combination Calculator (nCr)

URL: https://speedycalculator.com/calculators/statistics/combinations/
Last updated: 2026-10-25

> The combination calculator counts how many ways you can choose r items from n when order does not matter, nCr, and also gives combinations with repetition.

## Inputs

- Total items (n)
- Items chosen (r)

## Results

- Combinations
- With repetition
- Chance of one specific combination

## Formula

```
C(n, r) = n! ÷ (r! (n − r)!)
With repetition: C(n + r − 1, r)
```

## Explanation

Combinations answer questions like how many lottery tickets or committees are possible.

### How to use the Combination Calculator

- **Total items (n)**
- **Items chosen (r)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The factorial formula is computed using log-gamma so it works for large n.

### Inputs explained

FieldWhat to enterTotal items (n)A numberItems chosen (r)A number

### What each result means

- **Combinations** = comb([Total items (n)], [Items chosen (r)])
- **With repetition** = comb([Total items (n)] + [Items chosen (r)] - 1, [Items chosen (r)])
- **Chance of one specific combination** = 1÷[Combinations]×100

## Worked example

Inputs — Total items (n): 49; Items chosen (r): 6.

Results — **Combinations = 13983816**; With repetition = 25827165; Chance of one specific combination = 0.000007 %.

## FAQ

**What is the difference from permutations?**
Permutations count orderings; combinations ignore order.

**How many 6/49 lottery combinations are there?**
13,983,816.

**What formula does the Combination Calculator use?**
C(n, r) = n! ÷ (r! (n − r)!).


## Sources

- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)