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 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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