# Permutations in which n people can occupy r seats in a classroom in java

## Which n people can occupy r seats in a classroom in Java

Our Aim is to write a Java code to find all the possible permutations in which (n) people can occupy (r) number of seats in a classroom.

Suppose (n) number  students are looking to find (r) seats in a classroom so how will they do it . They will do it with simple formula which is given by

## n P r  =    n! / (n-r)! ### Problem Statement :

In a classroom some of the seats are already occupied by students and only a few seats are available in the classroom. The available seats are assumed as r and n number of students are looking for the seat. We need to find in how many different permutations n number of students can sit on r number of chairs.

### Algorithm

• Input number of students in n
• Input number of seats in r
• Use permutation formula { factorial(n) / factorial(n-r) }
• Print Output ### Java code

Run
```import java.util.*;
import java.io.*;

public class Main
{
public static void main(String[] args)
{

int n, r, per, fact1, fact2;

Scanner sc =  new Scanner(System.in);

System.out.println("Enter the Value of n: ");
n = sc.nextInt();

System.out.println("Enter the Value of r: ");
r = sc.nextInt();

fact1 = 1;

for (int i = n; i > 1; i=i-1)
{
fact1 = fact1 * i;  //calculating factorial (n!)
}

int number;

number = n - r;

fact2 = 1;

for (int i = number; i > 1; i=i-1)
{
fact2 = fact2 * i;  //calculating factorial ((n-r)!)
}

per = fact1 / fact2;  //calculating  nPr

System.out.println(per+" ways");
}
}```

### Output

```Enter number of people: 5
Enter number of seats: 9
Total possible arrangements: 120```

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