Java Program to Find the Value of Permutation (nPr) and Combination (nCr)

Java programs to find the value of $nPr$ and $nCr$ have been shown here. $nPr$, $nCr$ are referred as the permutation and combination respectively. Here $n$ is the total no of objects, $r$ is the no of objects taken at a time for arrangement and $r \leq n$. The formula to find $nPr$ and $nCr$ are given below.

 $nPr = \frac{n!}{(n-r)!}$

 $nCr = \frac{n!}{(n-r)! \cdot r!}$

Example:

Suppose $n = 7$ and $r = 5$

$7P5 = \frac{7!}{(7-5)!} = \frac{7!}{2!} = \frac{5040}{2} = 2520$

$7C5 = \frac{7!}{(7-5)!\cdot5!} = \frac{7!}{2!\cdot5!} = \frac{5040}{240} = 21$

Page content(s):

1. Program & output:

 1.1. Iterative approach

 1.2. Recursive approach

1. Program & output to find the value of permutation (nPr) and combination (nCr)

1.1. Java Program & output to find the value of permutation (nPr) and combination (nCr) using iteration

Code has been copied

/********************************
        alphabetacoder.com
Java Program to find permutation 
(nPr) and combination (nCr) 
*********************************/

import java.util.Scanner;
import java.lang.*;

class Main {
    // function to calculate factorial
    long factorial(int num) {
        // declare variables
        int i;
        long fact = 1;
        // calculate factorial
        for (i = 2; i <= num; i++)
            fact *= i;

        // return result
        return fact;
    }

    // function to calculate nCr
    long calculate_ncr(int n, int r) {
        // return result
        return factorial(n) / (factorial(n - r) * factorial(r));
    }

    // function to calculate nPr
    long calculate_npr(int n, int r) {
        // return result
        return factorial(n) / factorial(n - r);
    }

    public static void main(String[] args) {
        // declare instance of Scanner class
        Scanner sc = new Scanner(System.in);
        // declare object of class
        Main obj = new Main();
        // delclare variables
        int n, r;

        // take input of the number
        System.out.print("Enter the value of n: ");
        n = sc.nextInt();
        System.out.print("Enter the value of r: ");
        r = sc.nextInt();

        // display results by calling function
        System.out.println(n + "P" + r + " = " + obj.calculate_npr(n, r));
        System.out.println(n + "C" + r + " = " + obj.calculate_ncr(n, r));
    }
}

Output

Enter the value of n: 9

Enter the value of r: 2

9P2 = 72

9C2 = 36

1.2. Java Program & output to find the value of permutation (nPr) and combination (nCr) using recursion

Code has been copied

/************************************
          alphabetacoder.com
Java Program to find permutation(nPr) 
and combination (nCr) using recursion
*************************************/

import java.util.Scanner;
import java.lang.*;

class Main {
    // recursive function to calculate factorial
    long factorial(int num) {
        if (num <= 1)
            return 1;

        return num * factorial(num - 1);
    }

    // function to calculate nCr
    long calculate_ncr(int n, int r) {
        // return result
        return factorial(n) / (factorial(n - r) * factorial(r));
    }

    // function to calculate nPr
    long calculate_npr(int n, int r) {
        // return result
        return factorial(n) / factorial(n - r);
    }

    public static void main(String[] args) {
        // declare instance of Scanner class
        Scanner sc = new Scanner(System.in);
        // declare object of class
        Main obj = new Main();
        // delclare variables
        int n, r;

        // take input of the number
        System.out.print("Enter the value of n: ");
        n = sc.nextInt();
        System.out.print("Enter the value of r: ");
        r = sc.nextInt();

        // display results by calling function
        System.out.println(n + "P" + r + " = " + obj.calculate_npr(n, r));
        System.out.println(n + "C" + r + " = " + obj.calculate_ncr(n, r));
    }
}

Output

Enter the value of n: 7

Enter the value of r: 0

7P0 = 1

7C0 = 1