Ncr Calculator

How to Use the Combination (nCr) Calculator

This Combination (nCr) Calculator is a useful tool for finding the number of combinations in a set where the order does not matter. Follow these steps to efficiently use the calculator and determine the number of ways to choose items from a larger group.

Step-by-Step Guide

1. Enter the Total Number of Items (n): In the field labeled Total number of items (n), input the total number of items in the set. This number should be a whole number and must be between 0 and 170. Ensure no decimals or negatives are used.

2. Enter the Number of Items to Choose (r): In the field labeled Number of items to choose (r), input the number of items you wish to select from the total. Like the previous input, this must also be a whole number between 0 and 170. Again, fractional or negative numbers are not acceptable.

3. View the Results: Once both inputs are submitted, the calculator will automatically compute and display the following:

   • Number of Combinations (nCr): This value represents the total number of possible combinations of choosing r items from a set of n items. It is calculated using the formula nCr = factorial(n) / (factorial(r) * factorial(n – r)).

   • Formula Used: The calculator displays the formula of the combinations in the format C(n, r), helping you understand how the calculation reflects the problem setup.

   • Formula Expanded: For clarity, the expanded form of the formula is also shown as n!/(r!(n-r)!), providing a detailed breakdown of how the factorials contribute to the combination result.

Now, you should be able to easily compute the number of combinations for different scenarios using this efficient calculator!