Seating arrangement of N boys sitting around a round table such that two particular boys sit together

There are N boys which are to be seated around a round table. The task is to find the number of ways in which N boys can sit around a round table such that two particular boys sit together.
Examples: 

Input: N = 5 
Output: 12 
2 boy can be arranged in 2! ways and other boys 
can be arranged in (5 – 2)! (2 is subtracted because the 
previously selected two boys will be considered as a single boy now and No. of ways to arrange boys around a round table = (n-1)!) 
So, total ways are 2! * (n-2)!)  =  2! * 3! = 12
Input: N = 9 
Output: 10080

Approach:

• First, 2 boys can be arranged in 2! ways.
• No. of ways to arrange remaining boys and the previous two boy pair is (n – 2)!.
• So, Total ways = 2! * (n – 2)!.

Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the total count of ways
int Total_Ways(int n)
{

    // Find (n - 2) factorial
    int fac = 1;
    for (int i = 2; i <= n - 2; i++) {
        fac = fac * i;
    }

    // Return (n - 2)! * 2!
    return (fac * 2);
}

// Driver code
int main()
{
    int n = 5;

    cout << Total_Ways(n);

    return 0;
}

Java

// Java implementation of the approach
import java.io.*;

class GFG
{

// Function to return the total count of ways
static int Total_Ways(int n)
{

    // Find (n - 2) factorial
    int fac = 1;
    for (int i = 2; i <= n - 2; i++)
    {
        fac = fac * i;
    }

    // Return (n - 2)! * 2!
    return (fac * 2);
}

// Driver code
public static void main (String[] args)
{

    int n = 5;

    System.out.println (Total_Ways(n));
}
}

// This code is contributed by Tushil.

Python3

# Python3 implementation of the approach

# Function to return the total count of ways
def Total_Ways(n) :

    # Find (n - 2) factorial
    fac = 1;
    for i in range(2, n-1) :
        fac = fac * i;

    # Return (n - 2)! * 2!
    return (fac * 2);


# Driver code
if __name__ == "__main__" :

    n = 5;

    print(Total_Ways(n));

# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;

class GFG
{

// Function to return the total count of ways
static int Total_Ways(int n)
{

    // Find (n - 2) factorial
    int fac = 1;
    for (int i = 2; i <= n - 2; i++)
    {
        fac = fac * i;
    }

    // Return (n - 2)! * 2!
    return (fac * 2);
}

// Driver code
static public void Main ()
{
    int n = 5;

    Console.Write(Total_Ways(n));
}
}

// This code is contributed by ajit..

Javascript

<script>
// javascript implementation of the approach

    // Function to return the total count of ways
    function Total_Ways(n)
    {

        // Find (n - 2) factorial
        var fac = 1;
        for (i = 2; i <= n - 2; i++)
        {
            fac = fac * i;
        }

        // Return (n - 2)! * 2!
        return (fac * 2);
    }

    // Driver code
        var n = 5;
        document.write(Total_Ways(n));

// This code is contributed by aashish1995
</script>

Output

12

Time Complexity: O(n)
Auxiliary Space: O(1)