Guest

There are 10 halting stations on a circular road in a city. On the route, a bus will stop at any three stations so that no two stations are adjacent. The number of such possible bus routes are

There are 10 halting stations on a circular road in a city. On the route, a bus will stop at any three stations so that no two stations are adjacent. The number of such possible bus routes are

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
The idea you used to get the 35=(7c4) can be adapted to the circular case.
Cut the railway line just before a station, and straighten it out. Now we have 10 stops in a line. Either (i) we use neither of the two endstations, (5c4) ways; or else (ii) we use one endstation and therefore not the other.
If we select say the left endstation, then the next is forbidden, as is the other end. So we need to choose 3 stops from 7. This can be done in (5c3) ways.
That gives a total of (5c4)+2(5c3). The argument generalizes.

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free