# Number of ways to choose a pair containing an even and an odd number from 1 to N

Last Updated : 27 Jul, 2022

Given a number N the task is to find the number of pairs containing an even and an odd number from numbers between 1 and N inclusive.

Note: The order of numbers in the pair does not matter. That is (1, 2) and (2, 1) are the same.

Examples

```Input: N = 3
Output: 2
The pairs are (1, 2) and (2, 3).```
```Input: N = 6
Output: 9
The pairs are (1, 2), (1, 4), (1, 6), (2, 3),
(2, 5), (3, 4), (3, 6), (4, 5), (5, 6). ```

Approach: The number of ways to form the pairs is (Total number of Even numbers*Total number of Odd numbers).
Thus

1. if N is an even number of even numbers = number of odd numbers = N/2
2. if N is an odd number of even numbers = N/2 and the number of odd numbers = N/2+1

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `// Driver code` `int` `main()` `{` `    ``int` `N = 6;`   `    ``int` `Even = N / 2;`   `    ``int` `Odd = N - Even;`   `    ``cout << Even * Odd;`   `    ``return` `0;` `    ``// This code is contributed` `    ``// by ANKITRAI1` `}`

## Java

 `// Java implementation of the above approach` `import` `java.util.*;` `import` `java.lang.*;` `import` `java.io.*;` `class` `GFG{`   `// Driver code` `public` `static` `void` `main(String args[])` `{` `  ``int` `N = ``6``;` ` `  `  ``int` `Even = N / ``2` `;` ` `  `  ``int` `Odd = N - Even ;` `   `  `  ``System.out.println( Even * Odd );` `   `  `}` `}`

## Python3

 `# Python implementation of the above approach` `N ``=` `6`   ` ``# number of even numbers` `Even ``=` `N``/``/``2`   `# number of odd numbers` `Odd ``=` `N``-``Even ` `print``(Even ``*` `Odd)`

## C#

 `// C# implementation of the ` `// above approach` `using` `System;`   `class` `GFG` `{`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``int` `N = 6;` `    `  `    ``int` `Even = N / 2 ;` `    `  `    ``int` `Odd = N - Even ;` `        `  `    ``Console.WriteLine(Even * Odd);` `}` `}`   `// This code is contributed` `// by Akanksha Rai(Abby_akku)`

## PHP

 ``

## Javascript

 ``

Output:

`9`

Time Complexity: O(1)

Space Complexity: O(1)

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