Find nCr Through Programming Languages.

What is ⁿC_r in mathematics?

ⁿC_r is referred to as the combination. ⁿC_r is a selection of r objects from a set of n objects. 

Formula of  ⁿC_r

ⁿC_r = n!/(r!*(n-r)!)

Find ⁿC_r through programming languages such as C, C++, and Java.

We will try to solve this problem with the help of functions. We need to create a function to find the factorial of n, r, and (n-r)! and then create a function to calculate the value of  ⁿC_r.

Example of  ⁿC_r

Input:

The value of n is 8 

The value of r is 2

Output:

ⁿC_r = 28

Explanation:

The value of  ⁸C₂ is 28.

Code in C language

#include <stdio.h>

int factorial(int n){
    
    int fact = 1;
    
    for(int i=0; i<=n; i++){
        fact = fact * i;
    }
    
    return fact;
}

int nCr(int n, int r){
    
    int num = factorial(n);
    
    int denom = factorial(r) * factorial(n-r);
    
    int result = num/denom;
    
    return result;
}

int main()
{
    int n, r;
    
    printf("The value of n is ");
    scanf("%d", &n);
    
    printf("The value of r is ");
    scanf("%d", &r);

    int result = nCr(n,r);
    
    printf("%d",result);

    return 0;
}

Output:

The value of n is 8 

The value of r is 2

28

Code in C++ language

#include<iostream>
using namespace std;

int factorial(int n){
    
    int fact = 1;
    
    for(int i=0; i<=n; i++){
        fact = fact * i;
    }
    
    return fact;
}

int nCr(int n, int r){
    
    int num = factorial(n);
    
    int denom = factorial(r) * factorial(n-r);
    
    int result = num/denom;
    
    return result;
}

int main()
{
    int n, r;
    
    cout << "The value of n is ";
    cin>>n;
    
    cout << "The value of r is ";
    cin>>r;

    int result = nCr(n,r);
    
    cout<<result;

    return 0;
}

Output:

The value of n is 8 

The value of r is 2

28

Code in Java language

import java.util.Scanner; 

public class Main
{   
    static int factorial(int n){
    
        int fact = 1;
    
        for(int i=0; i<=n; i++){
            fact = fact * i;
        }
    
        return fact;
    }

    static int nCr(int n, int r){
    
        int num = factorial(n);
    
        int denom = factorial(r) * factorial(n-r);
    
        int result = num/denom;
    
        return result;
    }
    
	public static void main(String[] args) {
	    
	    Scanner s = new Scanner(System.in);
	    
		System.out.print("The value of n is ");
		int n = s.nextInt();
		
		System.out.print("The value of r is ");
		int r = s.nextInt();
		
		int result = nCr(n,r);
		
    	System.out.println(result);
		
	}
}

Output:

The value of n is 8 

The value of r is 2

28

Task: Try to find the value of nPr