Introduction

The task is to find the number of ways we can stop the train at K stations out of N stations between S1 and S2 such that the stopping stations are non-consecutive.

Program

def find( s, ts):
#select s non-consecutive station from ts number of stations "   
    temp, temp1  = 1, 1
    pos = s
    while s != 1:
        temp1 *= s
        s -= 1
    i = ts - pos + 1
    while i != (ts-2 * pos + 1):
        temp *= i
        i -= 1
    if (ts - pos + 1) >= pos:
        return int(temp/temp1)
    else:
        return -1
ip_stopping_stations = find(2, 14)
if ip_stopping_stations != -1:
    print("Number of ways: ",ip_stopping_stations)
else:
    print("Selection not possible!")

Output

Explanation

In the above code, we have used mathematical expression of combination ^(n-p+1)C_p where n is the number of station and p is the number of stopping stations.