Question

There are $p$ intermediate stations on a railway line from one terminus to other. In how many ways can a train stop at $3$ of these intermediate stations such that no two of them are consecutive?

• A. ${}^p{C}_3$
• B. ${}^{p-2}{C}_3$
• C. $p(p-1)$
• D. none of these

Answer 1

The correct option is B ${}^{p-2}{C}_3$

Number of intermediate stations$=P$

Let $1,2,3$ are stations to be stopped

$A$ and $B$ in between stops

$\Rightarrow$ Number of ways ${=}^{p-2}{C}_3$