C Program for Number of stopping station problem

There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?

Examples –

Input  : n = 12, s = 4
Output : 126

Input  : n = 16, s = 5
Output : 792

#include <stdio.h>
int stopping_station(int, int);

// function to calculate number
// of ways of selecting 'p' non consecutive
// stations out of 'n' stations
int stopping_station(int p, int n)
{

    int num = 1, dem = 1, s = p;

    // selecting 's' positions out of 'n-s+1'
    while (p != 1) {

        dem *= p;
        p--;
    }

    int t = n - s + 1;
    while (t != (n - 2 * s + 1)) {

        num *= t;
        t--;
    }

    if ((n - s + 1) >= s)
        printf("%d", num / dem);

    else

        // if conditions does not satisfy of combinatorics
        printf("not possible");
}

// driver code
int main()
{

    // n is total number of stations
    // s is no. of stopping stations
    int n, s;

    // arguments of function are
    // number of stopping station
    // and total number of stations
    stopping_station(4, 12);
}

Output:

126

Please refer complete article on Number of stopping station problem for more details!