Intermediate stations

[hey_thr67]

Between 2 junction stations X and Y there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is

a) 70
b) 126
c) 210
d) 420
e) 195

[mathbyvemuri]

If there are m stations and train should stop at n stations such that no two stoppages are adjacent to each other, the formula here is: (m-2)Cn.
In this case m = 12 and n = 4
So the answer shall be 10C4 = 210
Answer c
The explanation for a similar type of problem is given here:
https://mathbyvemuri.blogspot.in/2011/10 ... -2011.html