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? Choose the correct choice from the following answers:
A) 108
B) 112
C) 126
D) 140
E) None of these
Explanation :   Initially, let's remove the 4 stopping stations   Then we are left with 8 non-stopping stations (=12-4) as shown below   (non-stopping stations are marked as 1,2 ... 8)   Now there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations   such that no two stopping stations are consecutive   This can be done in 91264 ways   Hence, required number of ways = 91264   =((9)(8)(7)(6)/(4)(3)(2)(1))=126   Answer 126
<result>C</result>
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?