Combinations Calculator (nCr)

Explanation of the Calculator:

1. Input Fields:

   • n: Number of distinct objects (total objects).
   • r: Number of objects to choose (sample size).

2. Formula: The formula for combinations (nCr) is:

   $$C(n,r)=\frac{n!}{r!(n-r)!}$$

   This formula calculates the number of ways to choose r objects from n distinct objects without considering the order of selection.

3. Buttons:

   • Calculate: Performs the calculation using the combination formula.
   • Clear: Resets the input fields and results.

Example:

• If you input n = 5 (5 objects) and r = 2 (choose 2), the result will be calculated as: $$C(5,2)=\frac{5!}{2!(5-2)!}=\frac{120}{2\times 6}=10$$