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# Number of arrays of size N whose elements are positive integers and sum is K in C++

We are given two numbers n and k. We need to find the count of arrays that can be formed using the n numbers whose sum is k.

The number of arrays of size N with sum K is $\dbinom{k - 1}{n - 1}$.

This a straightforward formula to find the number arrays that can be formed using n elements whose sum k. Let's see an example.

**Input**

n = 1 k = 2

**Output**

1

The only array that can be formed is [2]

**Input**

n = 2 k = 4

**Output**

3

The arrays that can be formed are [1, 3], [2, 2], [3, 1].

## Algorithm

- Initialise the numbers n and k.
- Write a function to calculate the factorial of a number.
- Now, write our main function to compute the binomial as seen above.
- Return the answer.

## Implementation

Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h> using namespace std; int factorial(int n) { int result = 1; for (int i = 2; i <= n; i++) { result *= i; } return result; } int getNumberOfArraysCount(int n, int k) { return factorial(n) / (factorial(k) * factorial(n - k)); } int main() { int N = 5, K = 8; cout << getNumberOfArraysCount(K - 1, N - 1) << endl; return 0; }

## Output

If you run the above code, then you will get the following result.

35

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