C++ program to find permutation and combination npr and ncr

C++ program to find permutation and combination npr and ncr :

This C++ program will show you how to find the permutation and combination using user provided values. We will write one program that takes the values of n and r as input and find out the required output.

Formula to find permutation and combination :

Before moving to the program, let’s check the formule required to solve it.

Permutation and combination are calculated by considering n distinct elements r at a time. So, we will take the values of n and r from the user. Below is the formula to find out permutation :

P(n,r) = n!/(n-r)!

Similarly, we can calculate the value of combination using the below formula:

C(n,r) = n!/r!(n-r)!

! is used to define factorial.

As you can see, if we know how to find the factorial of a number, we can easily find out npr and ncr values of any two numbers.

C++ program to find permutation and combination:

#include <iostream>

using namespace std;

int findFact(int n)
{
    return n == 1 ? 1 : n * findFact(n - 1);
}

int findNpR(int n, int r)
{
    return findFact(n) / findFact(n - r);
}

int findNcR(int n, int r)
{
    return findFact(n) / (findFact(n - r) * findFact(r));
}

int main()
{
    int n, r, nPr, nCr;

    cout << "Enter the value of n:" << endl;
    cin >> n;

    cout << "Enter the value of r:" << endl;
    cin >> r;

    nPr = findNpR(n, r);
    nCr = findNcR(n, r);

    cout << "Permutation,nPr : "<< nPr << endl;
    cout << "Combination,nCr : "<< nCr << endl;
}

Explanation :

  • findFact method is used to find the factorial of a number.
  • findNpR and findNcR methods are used to find out the permutation and combination. It takes the values of n and r and returns the values of permutation and combination.

Sample output :

Enter the value of n:
10
Enter the value of r:
3
Permutation,nPr : 720
Combination,nCr : 120

You can try to run this application and find out permutation and combinations for different values.

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