Calculate nCr
About Combinations
Combinations, denoted as nCr or C(n,r), represent the number of ways to choose r items from a set of n distinct items without regard to the order of selection.
Formula
nCr = n! / (r! × (n-r)!)
Where n! (n factorial) = n × (n-1) × (n-2) × ... × 1
Example
If you have 5 different books and want to choose 3 of them to take on a trip, the number of different combinations is:
5C3 = 5! / (3! × (5-3)!) = 120 / (6 × 2) = 10
So there are 10 different ways to choose 3 books from 5.
Applications
- Probability calculations
- Statistical analysis
- Game theory and strategy
- Genetics and biology
- Computer science algorithms