# C++ Program to find Permutations in which n people can occupy r seats in a classroom

## Program to find Permutations in which n people can occupy r seats in a classroom

Here we will discuss how to find the number of ways N people can occupy R seats in a classroom in C++ programming language.

This is a problem specific program which deals with problems like in how many ways employees can be arranged in the seats available in a company or the same for the students in a school or college.

This problem can be easily solved by the use of the simple formula of permutations which is

nPr =    n! / (n-r)!

Example: we have 5 students and the total number of seats are 6.

Permutations             =    6P5

=    6! / (6-5)!

=    720.

So, there are 720 ways in which 5 students can be arranged in 6 seats. ### Working

Let’s see how the code works:

• User gives two inputs(number of people and seats).
• The inputs are stored in two int type variables say n(number of people) & r(number of seats).
• If the number is people are more than the number of seats then stop the program otherwise go to next step

if(r<n)

cout<<“Cannot adjust “<<n<<” people on “<<r<<” seats”;

return 0;

• Find all the possible arrangements using the formula of permutation

int p=fact(r)/fact(r-n);

• Print the output.

### C++ Code

`//C++ Program//Permutations in which n people can occupy r seats#include<iostream>using namespace std;//function for factorialint factorial(int num){	int fact=1;	for(int i=num;i>=1;i--)		fact*=i;	return fact;}//main programint main(){	int n,r;	cout<<"Enter number of people: ";	//user input	cin>>n;	cout<<"Enter number of seats: ";	//user input	cin>>r;	//if there are more people than seats	if(r<n)	{		cout<<"Cannot adjust "<<n<<" people on "<<r<<" seats";		return 0;	}	//finding all possible arrangements of n people on r seats	// by using formula of permutation	int p = factorial(r)/factorial(r-n);	//printing output	cout<<"Total arrangements: "<<p;	return 0;}`

#### Output

`Enter number of people: 5Enter number of seats: 6Total arrangements: 720`