Combination Calculator

Calculate combinations, combinations with repetition, and explore real-world applications

Combination Type

Select Combination Type

Select a combination type and enter values to calculate

Standard Combination: C(n,r) = n!/(r!(n-r)!)
Select r items from n without repetition

Combination with Repetition: C(n+r-1,r)
Select r items from n with repetition allowed

Key Property: C(n,r) = C(n,n-r)
Symmetry property

Committee Selection: Choose r people from n candidates
Order doesn't matter

Lottery Numbers: Select r numbers from 1 to n
Standard combination

Pizza Toppings: Choose r toppings from n available
With or without repetition

Multiset Combinations: Items with different quantities
Complex selection scenarios

Integer Partitions: Ways to sum to a number
Number theory applications

Probability: P(event) = favorable/total
Uses combinations for counting