Combination Calculator

What are Combinations?

A combination is a selection of objects where the order doesn't matter. C(n,r) represents the number of ways to choose r objects from n total objects.

Formula

C(n,r) = n! / (r! × (n-r)!)

Where: n ≥ r ≥ 0

Difference from Permutations

• Combinations: Order doesn't matter (choosing team members)
• Permutations: Order matters (arranging people in line)

Applications

• Lottery number selections
• Choosing committee members
• Selecting items from a menu
• Probability calculations

Examples

C(5,3): Ways to choose 3 people from 5 total

C(5,3) = 5!/(3!×2!) = 120/(6×2) = 10

C(10,2): Ways to choose 2 items from 10 total

C(10,2) = 10!/(2!×8!) = 45