Combination Calculator

Calculate the number of combinations (nCr) for unordered selections. This tool computes how many ways you can choose r items from a set of n items where order doesn't matter.

What are Combinations?

Combinations are selections of items from a larger set where the order doesn't matter. For example, choosing 3 people from a group of 10 for a committee is a combination problem because the order in which you select them doesn't change the committee composition.

Combination Formula

The formula for calculating combinations is:

C(n,r) = n! / (r! × (n-r)!)

Where:

• n = total number of items
• r = number of items to select
• ! = factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1)

How to Use This Calculator

1. Enter the total number of items (n) in the first field
2. Enter the number of items you want to select (r) in the second field
3. Click "Calculate Combination" to see the result
4. View the formula breakdown and final answer

Examples

• Lottery: How many ways can you choose 6 numbers from 49? C(49,6) = 13,983,816
• Committee: Selecting 3 people from 10 for a team? C(10,3) = 120
• Card games: Choosing 5 cards from a 52-card deck? C(52,5) = 2,598,960

Important Notes

• Both n and r must be non-negative integers
• r cannot be greater than n
• Order doesn't matter in combinations (unlike permutations)
• C(n,0) = 1 (there's one way to choose nothing)
• C(n,n) = 1 (there's one way to choose everything)