C# Program to Find nCr

This C# program calculates the combination value C(n, r), often referred to as “n choose r” or “nCr.” In combinatorial mathematics, C(n, r) represents the number of ways to choose r items from a set of n distinct items without regard to the order of selection. It is computed using the formula C(n, r) = n! / (r! * (n – r)!), where “!” denotes the factorial of a number.

Problem statement

Write a C# program that calculates the combination (nCr) of two non-negative integers, n and r.

C# Program to Find nCr

using System;

class Program
{
    // Function to calculate factorial of a number
    static int Factorial(int n)
    {
        if (n == 0)
            return 1;
        return n * Factorial(n - 1);
    }

    // Function to calculate nCr
    static int nCr(int n, int r)
    {
        return Factorial(n) / (Factorial(r) * Factorial(n - r));
    }

    static void Main()
    {
        Console.Write("Enter the value of n: ");
        int n = Convert.ToInt32(Console.ReadLine());

        Console.Write("Enter the value of r: ");
        int r = Convert.ToInt32(Console.ReadLine());

        if (n >= r && n >= 0 && r >= 0)
        {
            int result = nCr(n, r);
            Console.WriteLine($"The value of {n}C{r} is {result}");
        }
        else
        {
            Console.WriteLine("Invalid input. Make sure n >= r and both are non-negative.");
        }
    }
}

How it works

Here’s a step-by-step breakdown of how the program works:

Factorial Function:

Code:

static int Factorial(int n)
{
if (n == 0)
return 1;
return n * Factorial(n – 1);
}

• This function calculates the factorial of a given number n.
• It’s a recursive function. When n is 0, it returns 1 (since 0! = 1).
• Otherwise, it recursively multiplies n with the factorial of (n-1) until n becomes 0.

nCr Function:

Code:

static int nCr(int n, int r)
{
return Factorial(n) / (Factorial(r) * Factorial(n – r));
}

• This function uses the Factorial function to calculate the combination (nCr).
• It applies the combination formula: nCr = n! / (r! * (n - r)!).

User Input:

Code:

static void Main()
{
    Console.Write("Enter the value of n: ");
    int n = Convert.ToInt32(Console.ReadLine());

    Console.Write("Enter the value of r: ");
    int r = Convert.ToInt32(Console.ReadLine());
}

The Main method prompts the user to enter values for n and r using Console.ReadLine() and converts them to integers.

Input Validation:

Code:

if (n >= r && n >= 0 && r >= 0)
{
// Calculate nCr
}
else
{
Console.WriteLine(“Invalid input. Make sure n >= r and both are non-negative.”);
}

It checks if the input is valid. n must be greater than or equal to r and both must be non-negative.

Calculate nCr:

Code:

int result = nCr(n, r);
Console.WriteLine($”The value of {n}C{r} is {result}”);

• If the input is valid, it calculates the value of nCr using the nCr function and prints the result.

Output:

That’s how the program works! It takes user input for n and r, validates the input, calculates nCr if the input is valid, and displays the result. If the input is invalid, it provides an appropriate error message.

Input/Output