C program to calculate the value of nPr?

Permutations, nPr can also be represented as P(n,r), is a mathematical formula to find the number of ways to arrange r objects from n objects where order matters. The formula of P(n, r) is n! / (n − r)!.

The number of permutations on a set of n elements is given by n! where "!" represents factorial.

Syntax

nPr = n! / (n - r)!

Where:

• n is the total number of objects
• r is the number of objects to be selected
• ! denotes factorial

Example

Let's calculate P(5, 4) which means selecting and arranging 4 objects from 5 objects −

#include <stdio.h>

long int fact(int x) {
    int i;
    long int f = 1;
    for(i = 2; i <= x; i++) {
        f = f * i;
    }
    return f;
}

int main() {
    int n, r;
    long int npr;
    n = 5;
    r = 4;
    npr = fact(n) / fact(n - r);
    printf("P(%d, %d) = %ld<br>", n, r, npr);
    return 0;
}

P(5, 4) = 120

Explanation

The calculation works as follows:

P(5, 4) = 5! / (5-4)!
        = 5! / 1!
        = 120 / 1
        = 120

Where 5! = 1 × 2 × 3 × 4 × 5 = 120

Key Points

• nPr represents permutations where order matters
• The factorial function calculates n! = 1 × 2 × 3 × ... × n
• Use long int for larger factorial values to avoid overflow

Conclusion

The nPr formula efficiently calculates permutations by dividing n! by (n-r)!. This mathematical approach is useful in probability and combinatorics problems where arrangement order is significant.