OverIQ.com

  1. Home
  2. C Programming Examples
  3. C Program to calculate Permutation and Combination

C Program to calculate Permutation and Combination

Last updated on September 23, 2020

The following is a C program to compute Permutation and Combination:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
/**************************************************
 Program to calculate Permutation and Combination
 * 
 * Enter n: 10
 * Enter r: 4
 * Permutation = 5040
 * Combination = 210
 ***************************************************/

#include<stdio.h> // include stdio.h library
long permutation(int n, int r);
long combination(int n, int r);
long factorial(int num);

int main(void)
{    
    int n, r;

    printf("Enter n: ");
    scanf("%d", &n);

    printf("Enter r: ");
    scanf("%d", &r);

    printf("Permutation = %ld\n", permutation(n, r));    
    printf("Combination = %ld", combination(n, r));

    return 0; // return 0 to operating system
}

long permutation(int n, int r)
{
    return factorial(n) / factorial(n-r);
}

long combination(int n, int r)
{
    return permutation(n, r) / factorial(r);
}

long factorial(int num)
{
    long long fact = 1;

    while(num > 0)
    {
        fact *= num;
        num--;
    }

    return fact;
}

Try it now

Expected Output: 1st run:

1
2
3
4
Enter n: 5
Enter r: 3
Permutation = 60
Combination = 10

2nd run:

1
2
3
4
Enter n: 5
Enter r: 0
Permutation = 1
Combination = 1

How it works #

Nothing magical here we are simply using the formula to calculate permutation and combination.

The permutations of n different objects taken r at a time is given by:

\begin{gather*}
nPr = \frac{n!}{(n-r)!}
\end{gather*}

The combinations of n different objects taken r at a time is given by:

\begin{gather*}
nCr = \frac{n!}{r!(n-r)!}
\end{gather*}

Recommended Reading:

C Programming Examples

Recent Posts