Combination Calculator
Combination Calculator
계산 combinations, combinations with repetition, and explore real-world applications
Combination Type
결과
Combination Result
Step-by-Step Solution
Formula Used
Real-World Examples
Select a combination type and enter values to calculate
Combination Formulas & Applications
Basic Combinations
Standard Combination: C(n,r) = n!/(r!(n-r)!)
Select r items from n without repetition
Select r items from n without repetition
Combination with Repetition: C(n+r-1,r)
Select r items from n with repetition allowed
Select r items from n with repetition allowed
Key Property: C(n,r) = C(n,n-r)
Symmetry property
Symmetry property
Real-World Applications
Committee Selection: Choose r people from n candidates
Order doesn't matter
Order doesn't matter
Lottery 숫자s: Select r numbers from 1 to n
Standard combination
Standard combination
Pizza Toppings: Choose r toppings from n available
With or without repetition
With or without repetition
Advanced Concepts
Multiset Combinations: Items with different quantities
Complex selection scenarios
Complex selection scenarios
Integer Partitions: Ways to sum to a number
숫자 theory applications
숫자 theory applications
Probability: P(event) = favorable/total
Uses combinations for counting
Uses combinations for counting
Quick Combination Examples
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