# Number of ways to get even sum by choosing three numbers from 1 to N

Given an integer N, find the number of ways we can choose 3 numbers from {1, 2, 3 …, N} such that their sum is even.

Examples:

Input : N = 3 Output : 1 Explanation: Select 1, 2 and 3 Input : N = 4 Output : 2 Either select (1, 2, 3) or (1, 3, 4)

# Recommended: Please solve it on “*PRACTICE*” first, before moving on to the solution.

*PRACTICE*

To get sum even there can be only 2 cases:

- Take 2 odd numbers and 1 even.
- Take all even numbers.

If n is even, Count of odd numbers = n/2 and even = n/2. Else Count odd numbers = n/2 +1 and evne = n/2.

Case 1 – No. of ways will be : ^{odd}C_{2} * even.

Case 2 – No. of ways will be : ^{even}C_{3}.

So, total ways will be Case_1_result + Case_2_result.

## C++

`// C++ program for above implementation ` `#include <bits/stdc++.h> ` `#define MOD 1000000007 ` `using` `namespace` `std; ` ` ` `// Function to count number of ways ` `int` `countWays(` `int` `N) ` `{ ` ` ` `long` `long` `int` `count, odd = N / 2, even; ` ` ` `if` `(N & 1) ` ` ` `odd = N / 2 + 1; ` ` ` ` ` `even = N / 2; ` ` ` ` ` `// Case 1: 2 odds and 1 even ` ` ` `count = (((odd * (odd - 1)) / 2) * even) % MOD; ` ` ` ` ` `// Case 2: 3 evens ` ` ` `count = (count + ((even * (even - 1) * ` ` ` `(even - 2)) / 6)) % MOD; ` ` ` ` ` `return` `count; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 10; ` ` ` `cout << countWays(n) << endl; ` ` ` `return` `0; ` `} ` |

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## Java

`// java program for above implementation ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `static` `long` `MOD = ` `1000000007` `; ` ` ` ` ` `// Function to count number of ways ` ` ` `static` `long` `countWays(` `int` `N) ` ` ` `{ ` ` ` `long` `count, odd = N / ` `2` `, even; ` ` ` ` ` `if` `((N & ` `1` `) > ` `0` `) ` ` ` `odd = N / ` `2` `+ ` `1` `; ` ` ` ` ` `even = N / ` `2` `; ` ` ` ` ` `// Case 1: 2 odds and 1 even ` ` ` `count = (((odd * (odd - ` `1` `)) / ` `2` `) ` ` ` `* even) % MOD; ` ` ` ` ` `// Case 2: 3 evens ` ` ` `count = (count + ((even * (even ` ` ` `- ` `1` `) * (even - ` `2` `)) / ` `6` `)) ` ` ` `% MOD; ` ` ` ` ` `return` `(` `long` `)count; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `static` `public` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `n = ` `10` `; ` ` ` ` ` `System.out.println(countWays(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

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## Python3

`# Python3 code for above implementation ` ` ` `MOD ` `=` `1000000007` ` ` `# Function to count number of ways ` `def` `countWays( N ): ` ` ` `odd ` `=` `N ` `/` `2` ` ` `if` `N & ` `1` `: ` ` ` `odd ` `=` `N ` `/` `2` `+` `1` ` ` `even ` `=` `N ` `/` `2` ` ` ` ` `# Case 1: 2 odds and 1 even ` ` ` `count ` `=` `(((odd ` `*` `(odd ` `-` `1` `)) ` `/` `2` `) ` `*` `even) ` `%` `MOD ` ` ` ` ` `# Case 2: 3 evens ` ` ` `count ` `=` `(count ` `+` `((even ` `*` `(even ` `-` `1` `) ` `*` ` ` `(even ` `-` `2` `)) ` `/` `6` `)) ` `%` `MOD ` ` ` `return` `count ` ` ` `# Driver code ` `n ` `=` `10` `print` `(` `int` `(countWays(n))) ` ` ` `# This code is contributed by "Sharad_Bhardwaj" ` |

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## C#

`// C# program for above implementation ` `using` `System; ` ` ` `public` `class` `GFG { ` ` ` ` ` `static` `long` `MOD = 1000000007; ` ` ` ` ` `// Function to count number of ways ` ` ` `static` `long` `countWays(` `int` `N) ` ` ` `{ ` ` ` `long` `count, odd = N / 2, even; ` ` ` ` ` `if` `((N & 1) > 0) ` ` ` `odd = N / 2 + 1; ` ` ` ` ` `even = N / 2; ` ` ` ` ` `// Case 1: 2 odds and 1 even ` ` ` `count = (((odd * (odd - 1)) / 2) ` ` ` `* even) % MOD; ` ` ` ` ` `// Case 2: 3 evens ` ` ` `count = (count + ((even * (even ` ` ` `- 1) * (even - 2)) / 6)) ` ` ` `% MOD; ` ` ` ` ` `return` `(` `long` `)count; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `static` `public` `void` `Main () ` ` ` `{ ` ` ` `int` `n = 10; ` ` ` ` ` `Console.WriteLine(countWays(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

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## PHP

`<?php ` `// PHP program for ` `// above implementation ` ` ` `$MOD` `= 1000000007; ` ` ` `// Function to count ` `// number of ways ` `function` `countWays(` `$N` `) ` `{ ` ` ` `global` `$MOD` `; ` ` ` ` ` `$count` `; ` ` ` `$odd` `=` `$N` `/ 2; ` ` ` `$even` `; ` ` ` `if` `(` `$N` `& 1) ` ` ` `$odd` `= ` `$N` `/ 2 + 1; ` ` ` ` ` `$even` `= ` `$N` `/ 2; ` ` ` ` ` `// Case 1: 2 odds ` ` ` `// and 1 even ` ` ` `$count` `= (((` `$odd` `* (` `$odd` `- 1)) / 2) * ` ` ` `$even` `) % ` `$MOD` `; ` ` ` ` ` `// Case 2: 3 evens ` ` ` `$count` `= (` `$count` `+ ((` `$even` `* (` `$even` `- 1) * ` ` ` `(` `$even` `- 2)) / 6)) % ` `$MOD` `; ` ` ` ` ` `return` `$count` `; ` `} ` ` ` ` ` `// Driver Code ` ` ` `$n` `= 10; ` ` ` `echo` `countWays(` `$n` `); ` ` ` `// This code is contributed by anuj_67. ` `?> ` |

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Output:

60

This article is contributed by **Sahil Chhabra**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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