Question

There are three routes; air, rail and road for going from Chennai to Hyderabad. But from Hyderabad to Vikarabad, there are two routes, rail and road. The number of routes from Chennai to Vikarabad via Hyderabad is
A. 4
B. 5
C. 6
D. 7

Answer 1

Hint: To find the number of routes from Chennai to Vikarabad via Hyderabad, let us denote A, B and C as the routes from Chennai to Hyderabad and D and E as the routes from Hyderabad to Vikarabad. We have to form a combination with these routes such that each combination should contain one route from A, B and C and another route from D and E. We can get the combinations as AD, AE, BD, BE, CD and CE.

Complete step-by-step answer:
We have to find the number of routes from Chennai to Vikarabad via Hyderabad. It is given that to travel from Chennai to Hyderabad, three routes can be opted. These are air, rail and road. This us denote these routes as A, B and C.
Now, we are given that to travel from Hyderabad to Vikarabad, the number of routes are 2. Let us denote these as D and E.

Now, we have to form a combination with these routes such that each combination should contain one route from A, B and C and another route from D and E.
We can get the combinations as AD, AE, BD, BE, CD and CE. These form the routes from Chennai to Vikarabad via Hyderabad.
Hence, the number of routes from Chennai to Vikarabad via Hyderabad is 6.

So, the correct answer is “Option C”.

Note: You may make mistake by adding the number of routes from Chennai to Hyderabad and that from Hyderabad to Vikarabad. This problem can also be solved in an alternate method as shown below.
We have, number of routes from Chennai to Hyderabad = 3
Number of routes from Hyderabad to Vikarabad = 2
We can use the fundamental law of multiplication here. This law states that if there are a ways of doing something and b ways of doing another thing, then there are $a\times b$ ways of performing both actions.
Hence, number of routes from Chennai to Vikarabad via Hyderabad $=3\times 2=6$