0QUESTION: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?
ANSWER: 126
EXPANATION:Initially, let's remove the 4 stopping stations
Then we are left with 8 non-stopping stations (=12-4)
Now there are 9 positions to place the 4 stopping stations
such that no two stopping stations are consecutive
This can be done in 9C4 ways
Hence, required number of way= 9C4 =126
