Question

To travel from a place A to place B, there are two different bus routes B , B two different train routes T , T and one air route A. From place B to place C there is one bus route say B ‘ , two different train routes say T ‘ , T ‘ and one air route A ‘. Find the number of routes of commuting from place A to place C via place B without using similar mode of transportation.

Answer 1

From the above diagram the number of routes from A to C 

= (2 × 2 + 2 × 1) + [(2 × 1) + (2 × 1)] + [(1 × 1) + (1 × 2)] 

= 4 + 2 + 2 + 2 + 1 + 2 = 13