Gate Applied Course Test Series

Question

There are 20 intermediate stops on a route of a transport corporation bus. The number of ways in which the bus can stop at 6 of these intermediate stops such that no 2 stops are consecutive is ?

Answer 1

Number of stopping stations = 6

Number of non-stopping stations = 14

If we lay down the 14 non-stopping stations then we will have 15 choices where the stopping stations can be and none of them would be consecutive.

*	1	*	2	*	3	*	4	*	5	*	6	*	7	*	8
*	9	*	10	*	11	*	12	*	13	*	14	*

Here * are free positions and numbers are non-stopping stations. 

So we have to select 6 places from 15,

i.e., $${15\choose6} = \frac{15\times14\times13\times12\times11\times10}{6\times5\times4\times3\times2\times1} = 5005$$