C program to calculate the value of nPr for a given value of n & r

Arushi Dwivedi | April 4, 2021 | C Programming Example | No Comments

In this C Programming example, we will implement the program to find the value of nPr for a given value of n & r and print the output on the console.

Table of Contents

1. What is nPr in Probability – Mathematics?

nPr is a probability function that represents permutations. nPr represents the probability of selecting an ordered set of ‘r’ objects from a group of ‘n’ number of objects. The order of objects matters in the case of permutation. The formula to calculate nPr is –

nPr(n,r) = n! / (n-r)!
Here,
n = the total number of items or net size.
r = It is the subnet size or total number of items chosen from sample. 

n! is factorial(n) which is represented as 1*2*....*(n-1)*n
Similary the explanation for (n-r)! is also same.

Example:

Input 
n: 4
r: 3

Formula
4!/(4-3)! = 24/1 = 24

Output
4P3 is 24

Helpful topics to understand this program better are-

2. C Program to find the value of nPr for a given value of n & r

Let’s discuss the execution(kind of pseudocode) for the program to find the value of nPr for a given value of n & r in C.

Initially, the program will prompt the user to enter the values of n and r and then pass those values to the nPr(n, r) function.
In the int nPr(int n, int r) function, the factorial of the values are calculated using the int fact(int n) function.
After calculating the factorial the output is returned and printed on the console.

In this C Programming example, we have discussed how to find the value of nPr for a given value of n & r in C.

#include <stdio.h>

int fact(int n) {
  if (n <= 1) {
    return 1;
  }
  return n * fact(n - 1);
}

int nPr(int n, int r) { return fact(n) / fact(n - r); }

int main() {
  int n, r;
  printf("Enter the value of n: ");
  scanf("%d", &n);
  printf("Enter the value of r: ");
  scanf("%d", &r);

  printf("The value of %dP%d is %d", n, r, nPr(n, r));
  return 0;
}

Note: Only whole positive integer numbers are valid.

Output
Enter the value of n: 5
Enter the value of  r: 2
The value of 5P2 is 20

3. Conclusion

In this C Programming example, we have discussed how to find the value of nPr for a given value of n & r and discussed the steps of the program in detail.

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