There are $12$ stations between $A$ and $B$ . Find the number of ways in which a train can be made to stop at four of these intermediate stations, so that no two stations are consecutive?

126

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108

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112

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140

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Solution

The correct option is A $126$
Total number of station where train is stopping is 4.
Total number of stations where train is not stopping = 8

$X$ = non stopping station
$__X_{1}__X_{2}__X_{3}__X_{4}__X_{5}__X_{6}__X_{7}__X_{8}__$

So if we arrange all stations where train is not stopping linearly then there will be 9 positions to place 4 stations in between them.
so we have $_{4}^{9} C = 126$ ways.

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There are 12 stations between A and B. Find the number of ways in which a train can be made to stop at four of these intermediate stations, so that no two stations are consecutive?

There are $12$ stations between $A$ and $B$ . Find the number of ways in which a train can be made to stop at four of these intermediate stations, so that no two stations are consecutive?