Question

There are $12$ railway stations in a railway line. A train stops at $4$ stations randomly. Then probability that exactly three of them are consecutive is

• A. $\frac{17}{55}$
• B. $\frac{9}{55}$
• C. $\frac{8}{55}$
• D. $\frac{1}{55}$

Answer 1

Answer: (C)

Let A be the event that out of $4$ stations $3$ are consecutive.
$\therefore n\left(A\right)=2\times 8+8\times 7$
$=16+56$
$=72$

[Out of $4$ stations there are $2$ ways in which three consecutive stations occurs]
$n\left(S\right)$ = Ways of selected $4$ stations out of $12={}^{12}{C}_4$
$\therefore P\left(A\right)=\frac{72\times 4\cdot 3\cdot 2\cdot 1}{12\times 11\times 10\times 9}=\frac{8}{55}$