Combination calculator

Calculate combinations without repetition using n choose k. Select k items from n when order does not matter, with exact results for up to 1,000 items.

Result

Enter your data and run the tool. Your result will appear here.

Complementary choices

Compare choosing what to keep with choosing what to leave out.

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How to use the tool

Fill in these fields: Total items n (0–1000), Selected items k.
Select “Calculate” to obtain the result.
Count selections without order or repetition.
Integers with 0 ≤ k ≤ n ≤ 1000.
n=10 and k=3 gives 120; k=0 gives 1.
Exact integer result.
Compare choosing what to keep with choosing what to leave out.
One possible selection, with the chosen items highlighted.

Method and principles

Formula

C(n,k) = \frac{n!}{k! \times (n - k)!}

Example and interpretation

Combinations count selections where order does not change the group and each item can appear only once. Choosing 2 people from 5 gives 10 pairs: Anna and Luca form the same pair as Luca and Anna. If order matters, use a different model rather than applying this result to arrangements or sequences.

Practical example

Input

Total items n (0–1000): 10
Selected items k: 3

Result

\frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120

Calculation steps

Substitute the example values into the formula.
$C(n,k) = \frac{10!}{3! \times (10 - 3)!}$

Limits and checks

Limits and checks
Parameter	Value
Total items n (0–1000)	≥ 0; ≤ 1000
Selected items k	≥ 0; ≤ 1000

Combination calculator

Set your data

Result

Complementary choices

How to use the tool

Method and principles

Formula

Example and interpretation

Practical example

Calculation steps

Limits and checks

Favorites

Combination calculator

Set your data

Result

How to use the tool

Method and principles

Formula

Example and interpretation

Practical example

Calculation steps

Limits and checks

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