# 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

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.   ## Algorithm:-

1. User gives two inputs(number of people and seats).
2. The inputs are stored in two int type variables say n(number of people) & r(number of seats).
3. 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;

4. Find all the possible arrangements using the formula of permutation

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

5. Print the output. ## C++ Code:-

`   //C++ Program    //Permutations in which n people can occupy r seats    #include    using namespace std;    //function for factorial    int factorial(int num)    {        int fact=1;        for(int i=num;i>=1;i--)            fact*=i;        return fact;    }    //main program    int 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: 5    Enter number of seats: 6    Total arrangements: 720` • Highest Common Factor(HCF): C | C++Java | Python
• Lowest Common Multiple (LCM) : C | C++ | Java | Python
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