Question

There are $8$ intermediate stations on a railway line from one terminus to another. Find the number of ways in which a train can stop at $3$ stations such that two of the stations are consecutive.

• A. $32$
• B. $36$
• C. $30$
• D. $18$

Answer 1

The correct option is C $30$

When train stops at $1$st two stations, it can not stop at the third station.
Therefore, no. of ways for train to stop at other stations $=5$

When train stops at $2$nd and $3$rd station then, it can not stop at the $1$st and the $4$th station.
Therefore, no. of ways for the train to stop at other stations $=4$

Similarly, if the train stops at the $3$rd and $4$th station, no. of ways for train to stop at other stations $=4$
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For the train to stop at $7$th and $8$th station, no. of ways for train to stop at other stations $=5$

Total possibilities $=5\times 2+4\times 5=30$