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Q.

There are 10 intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at 3 of these intermediate stations so that no two of these halting stations are consecutive, is

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a

120

b

26

c

56

d

20

answer is A.

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Detailed Solution

$Total no . of stations = n = 10$

$Number of non consecutive halting stations = 3 \Rightarrow r = 3$

$No . of ways of selecting 3 non consecutive stations = n - r + 1_{C_{r}} = 8_{C_{3}} = 56$

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