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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
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B
36
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C
30
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D
18
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Solution

The correct option is C 30
When train stops at 1st 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 2nd and 3rd station then, it can not stop at the 1st and the 4th station.
Therefore, no. of ways for the train to stop at other stations =4

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



For the train to stop at 7th and 8th station, no. of ways for train to stop at other stations =5

Total possibilities =5×2+4×5=30

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