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Condition for Two Lines to Be Perpendicular

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Question

There are $10$ stations on a circular path. A train has to stop at $3$ stations such that no two stations are adjacent. The number of such selections must be?

A

50

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B

84

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C

126

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D

None of these

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Solution

The correct option is A $84$
$\begin{matrix} I f n o . t w o s t a t i o n a r e a d j a c e n t t h e n 9 p o i n t s A t r a i n h a s t o s t o p a t 3 s t a t i o n s T h e n r e q u i r e d s e l e c t i o n i s [h_{c r} = \frac{n!}{(n - r)! r!}] 9 |! 3 = \frac{91}{(9 - 3)! 3!} = 84 \end{matrix}$

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Condition for Two Lines to Be Perpendicular

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