Given an array arr[] of n integers and an integer K, the task is to find the number of ways to select exactly K even numbers from the given array.

**Examples: **

_Input: __arr[] = {1, 2, 3, 4} k = 1 _

Output:_ 2 _

Explanation:

The number of ways in which we can select one even number is 2.

_Input: _arr[] = {61, 65, 99, 26, 57, 68, 23, 2, 32, 30} k = 2

Output:10

Explanation:

The number of ways in which we can select 2 even number is 10.

Approach:  The idea is to apply the rule of combinatorics. For choosing r objects from the given n objects, the total number of ways of choosing is given by nCr. Below are the steps:

1. Count the total number of even elements from the given array(say cnt).
2. Check if the value of K is greater than cnt then the number of ways will be equal to 0.
3. Otherwise, the answer will be** nCk**.

Below is the implementation of the above approach:

• CPP

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// C++ program for the above approach

#include <bits/stdc++.h>

**using** **namespace** std;

**long** **long** f[12];

// Function for calculating factorial

**void** fact()

{

// Factorial of n defined as:

// n! = n * (n - 1) * ... * 1

f[0] = f[1] = 1;

**for** (``**int** i = 2; i <= 10; i++)

f[i] = i * 1LL * f[i - 1];

}

// Function to find the number of ways to

// select exactly K even numbers

// from the given array

**void** solve(``**int** arr[], **int** n, **int** k)

{

fact();

// Count even numbers

**int** even = 0;

**for** (``**int** i = 0; i < n; i++) {

// Check if the current

// number is even

**if** (arr[i] % 2 == 0)

even++;

}

// Check if the even numbers to be

// choosen is greater than n. Then,

// there is no way to pick it.

**if** (k > even)

cout << 0 << endl;

**else** {

// The number of ways will be nCk

cout << f[even] / (f[k] * f[even - k]);

}

}

// Driver Code

**int** main()

{

// Given array arr[]

**int** arr[] = { 1, 2, 3, 4 };

**int** n = **sizeof** arr / **sizeof** arr[0];

// Given count of even elements

**int** k = 1;

// Function Call

solve(arr, n, k);

**return** 0;

}

Output:

2

Time Complexity: O(N)

Auxiliary Space: O(N)

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#arrays #combinatorial #dynamic programming #mathematical #combionatrics #permutation and combination #school-programming