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Classical Definition of Probability

There are m-s...

Question

There are m-stations on a railway line. A train has to stop at 3 intermediate stations. Then probability that no two stopping stations are adjacent is

A

\frac{1}{m c_{3}}

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B

\frac{3}{m c_{3}}

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C

\frac{m - 2_{C_{3}}}{m c_{3}}

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D

\frac{m c_{2}}{m c_{3}}

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Solution

The correct option is C $\frac{m - 2_{C_{3}}}{m c_{3}}$
Let 3-stopping stations be $S_{1}, S_{2}, S_{3}$ . Then there are m-3 stations remaining. Between these m-3 stations there are m-2 places. Select any 3 for $S_{1}, S_{2}, S_{3}$ , Then no two stopping stations are adjacent
$P (E) = \frac{m - 2_{C_{2}}}{m_{C_{3}}}$

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