Combination with Replacement Calculator

Explanation of the Calculator:

1. Input Fields:

   • n: Number of distinct objects to choose from.
   • r: The size of the sample.

2. Formula: The combination with replacement formula is:

   $$C^R(n,r)=\frac{(n+r-1)!}{r!(n-1)!}$$

   This formula calculates the number of ways to choose r elements from n distinct elements where repetition of elements is allowed.

3. Buttons:

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

Example:

• If you input n = 5 (5 objects) and r = 3 (sample size of 3), the result will be calculated as: $$C^R(5,3)=\frac{(5+3-1)!}{3!(5-1)!}=\frac{7!}{3!4!}=35$$