# C++ Program to Compute Combinations using Factorials

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This is a C++ to compute combinations using factorials.

Problem Description

1. This algorithm prints a total number of combination possible for given n and r value.
2. The time complexity of this algorithm is O(n).

Problem Solution

1. This algorithm takes the input of n and r value.
2. Print the result using ( n! / (r! * (n-r)!)).
3. Exit.

Program/Source Code

C++ Program to compute combinations using factorials.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>

using namespace std;

// A function to find the factorial.
int factorial(int n)
{
int i;
for(i = n-1; i > 1; i--)
n *= i;

return n;
}

int main()
{
int n, r,  result;
cout<<"A program to find combination from nCr format using ( n! / (r! * (n-r)!))";
cout<<"\n\n\tEnter the value of n: ";
cin>>n;
cout<<"\tEnter the value of r: ";
cin>>r;

// Get result using formula to calculate combinations.
result = factorial(n)/(factorial(r)*factorial(n-r));

cout<<"\nThe number of possible combinations is: "<<result;
}```
Program Explanation

1. Take the input of n and r.
2. Using factorial(), calculate values for n!, r! and (n-r)!.
3. Using ( n! / (r! * (n-r)!)), print the result.
4. Exit.

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Runtime Test Cases
```Case 1:
A program to find combination from nCr format using ( n! / (r! * (n-r)!))

Enter the value of n: 5
Enter the value of r: 3

The number of possible combinations is: 10

Case 2:
A program to find combination from nCr format using ( n! / (r! * (n-r)!))

Enter the value of n: 13
Enter the value of r: 4

The number of possible combinations is: 221```

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