Java 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

Java

// Java code to calculate number
// of ways of selecting 'p' non
// consecutive stations out of
// 'n' stations

import java.io.*;
import java.util.*;

class GFG {
    public static 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)
            System.out.print(num / dem);

        else
            // if conditions does not satisfy of combinatorics
            System.out.print("not possible");

        return 0;
    }

    public static void main(String[] args)
    {
        // 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);
    }
}
// ""This code is contributed by Mohit Gupta_OMG ""

Output:

126

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

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