Question

If there are $10$ stations on a route and the train has to be stopped at $4$ them, then the number of ways in which the train can be stopped so that atleast two stopping stations are consecutive is :

• A. ${}^7{C}_4$
• B. ${}^{10}{C}_4{-}^8{C}_3$
• C. ${}^{10}{C}_4{-}^7{C}_3$
• D. ${}^9{C}_3$

Answer 1

The correct option is D ${}^9{C}_3$

The number of ways in which the train can be stopped so that atleast two stopping stations are consecutive is

Let two consecutive stations be a single unit then

Required answer will be ${}^9{\text{C}}_3$