Question

There are $12$ intermediate stations on a railway line from one terminus to another. Number of ways in which a train can stop at 5 of these intermediate stations, if no two of these stopping stations are to be consecutive

• A. $56$
• B. $495$
• C. $792$
• D. $70$

Answer 1

The correct option is A $56$

Let us $1st$ fix the last $4$ stops at $6,8,10,12$ then for $1st$ stop we have $4$ possibilities as it cannot be continuous. Now leaving last three stops and moving $4th$ one to $5th$ place we have $3$ opportunities. We go on till it gives $1$ opportunity.

Similarly we go on changing the position of stops and adding all the combination we will get $56.$

Hence, the answer is $56.$