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

Answer 1

We have three routes from Chennai to Hyderabad and two routes from Hyderabad to Vikarabad. To find the number of routes from Chennai to Vikarabad via Hyderabad can be given by the number of elements of the matrix formed by the combination of the routes from Chennai to Hyderabad and Hyderabad to Vikarabad.

Complete step-by-step answer:
Step 1:
We are given that the number of routes from Chennai to Hyderabad is three
They are air ,rail and road
Let us denote these routes by A , B , C
Step 2 :
And we are given that the number of routes from Hyderabad to Vikarabad is 2
They are rail and road
Lets us denote it by D , E
Step 3:
Now let's form combinations with the routes above.
The combination should consist of one route from step 1 and one from step 2
Let us construct a matrix which will help us with the combinations
\begin{gathered} {\text{ }}\begin{array}{*{20}{c}} A&{{\text{ }}B}&{{\text{ }}C} \end{array} \\\ \begin{array}{*{20}{c}} D \\\ E \end{array}{\text{ }}\left[ \begin{gathered} \begin{array}{*{20}{c}} {AD}&{BD}&{CD} \end{array} \\\ \begin{array}{*{20}{c}} {AE}&{BE}&{CE} \end{array} \\\ \end{gathered} \right] \\\ \end{gathered}
Step 4 :
The elements of the above matrix are the different routes .
So the number of elements gives us the number of routes from Chennai to Hyderabad via Vikarabad
The number of elements is 6
Therefore the number of routes is 6

Note: There is another easy alternative method to solve the problem
We are given three routes from Chennai to Hyderabad and the return route from Hyderabad to Vikarabad is 2.
So the number of routes are given by 3 * 2 = 6