Advanced Combination Calculator (nCr)
How to Use:
- Enter the total number of items to choose from (n) in the first field. This must be a non-negative integer.
- Enter the number of items to choose (r) in the second field. This must be a non-negative integer, and r cannot be greater than n.
- Click the "Calculate Combinations" button.
- The total number of unique combinations (nCr) will be displayed.
- Click "Show Details" to view the formula, theory, and a step-by-step calculation.
- Use "Clear All" to reset the calculator.
Calculation Result:
Number of Combinations C(n, r): -
Formula Used:
C(n, r) = n! / (r! * (n-r)!)
Theory:
A combination is a selection of items from a larger set where the order of selection does not matter. The formula C(n, r) calculates how many different ways you can choose 'r' items from a set of 'n' items.
For example, if you choose 2 letters from {A, B, C}, the combinations are {A,B}, {A,C}, and {B,C}. {B,A} is the same combination as {A,B}.
The '!' symbol denotes a factorial (e.g., 5! = 5 * 4 * 3 * 2 * 1).