# Seating arrangement of n boys and girls alternatively around a round table

There are n boys and n girls are to be seated around a round table, in a circle. The task is to find number of ways in which n boys and n girls can sit alternatively aound a round table. Given n<10

Examples:

```Input: n = 5
Output: 2880

Input: n = 1
Output: 1
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. First find the total number of ways in which boys can be arrange on round table.
No. of ways to arrange boys on table = (n-1)!
2. After making boys arrangement, now make arrangement for girls. As after seating boys there are n space available between them. So there are n position and n number of girls. So total number of arrangement in which girls sit between boys are n!.
3. Therefore Total number of ways = (number of arrangement of boys) * (number of ways to sit girl among boys) = (n-1)! * (n!)

Below is the implementation of the above approach:

## C++

 `// C++ program to find number of ways in which ` `// n boys and n girls can sit alternatively ` `// sound a round table. ` `#include ` `using` `namespace` `std; ` ` `  `#define ll long int ` ` `  `int` `main() ` `{ ` ` `  `    ``// Get n ` `    ``ll n = 5; ` ` `  `    ``// find fac1 = (n-1)! ` `    ``ll fac1 = 1; ` `    ``for` `(``int` `i = 2; i <= n - 1; i++) ` `        ``fac1 = fac1 * i; ` ` `  `    ``// Find fac2 = n! ` `    ``ll fac2 = fac1 * n; ` ` `  `    ``// Find total number of ways ` `    ``ll totalWays = fac1 * fac2; ` ` `  `    ``// Print the total number of ways ` `    ``cout << totalWays << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find number of ways ` `// in which n boys and n girls can sit  ` `// alternatively sound a round table. ` `import` `java .io.*; ` ` `  `class` `GFG ` `{ ` `public` `static` `void` `main(String[] args) ` `{ ` ` `  `    ``// Get n ` `    ``long` `n = ``5``; ` ` `  `    ``// find fac1 = (n-1)! ` `    ``long` `fac1 = ``1``; ` `    ``for` `(``int` `i = ``2``; i <= n - ``1``; i++) ` `        ``fac1 = fac1 * i; ` ` `  `    ``// Find fac2 = n! ` `    ``long` `fac2 = fac1 * n; ` ` `  `    ``// Find total number of ways ` `    ``long` `totalWays = fac1 * fac2; ` ` `  `    ``// Print the total number of ways ` `    ``System.out.println(totalWays); ` `} ` `} ` ` `  `// This code is contributed ` `// by anuj_67.. `

## Python3

 `# Python3 program to find number  ` `# of ways in which n boys and n  ` `# girls can sit alternatively  ` `# sound a round table. ` ` `  `# Get n  ` `n ``=` `5` ` `  `# find fac1 = (n-1)!  ` `fac1 ``=` `1` `for` `i ``in` `range``(``2``, n): ` `    ``fac1 ``=` `fac1 ``*` `i ` ` `  `# Find fac2 = n!  ` `fac2 ``=` `fac1 ``*` `n ` ` `  `# Find total number of ways ` `totalWays ``=` `fac1 ``*` `fac2 ` ` `  `# Print the total number of ways  ` `print``(totalWays) ` ` `  `# This code is contributed  ` `# by sahilshelangia `

## C#

 `// C# program to find number of ways ` `// in which n boys and n girls can sit  ` `// alternatively sound a round table. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `public` `static` `void` `Main() ` `{ ` ` `  `    ``// Get n ` `    ``long` `n = 5; ` ` `  `    ``// find fac1 = (n-1)! ` `    ``long` `fac1 = 1; ` `    ``for` `(``int` `i = 2; i <= n - 1; i++) ` `        ``fac1 = fac1 * i; ` ` `  `    ``// Find fac2 = n! ` `    ``long` `fac2 = fac1 * n; ` ` `  `    ``// Find total number of ways ` `    ``long` `totalWays = fac1 * fac2; ` ` `  `    ``// Print the total number of ways ` `    ``Console.WriteLine(totalWays); ` `} ` `} ` ` `  `// This code is contributed ` `// by Akanksha Rai(Abby_akku) `

## PHP

 `

Output:

```2880
```

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