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Ram can travel from Delhi to Mumbai either by 2 different trains or by 3 different buses or by 1 plane whereas he can travel from Mumbai to Andaman by two different planes.In how many ways he can reach Andaman from Delhi via Mumbai?

Ram can travel from Delhi to Mumbai either by 2 different trains or by 3 different buses or by 1 plane whereas he can travel from Mumbai to Andaman by two different planes.In how many ways he can reach Andaman from Delhi via Mumbai? Correct Answer 12

Concept:  

Fundamental principal of multiplication:

Let us suppose there are two tasks A and B such that the task A can be done in m different ways following which the second task B can be done in n different ways. Then the number of ways to complete the task A and B in succession respectively is given by: m × n ways

Fundamental principal of addition:

Let us suppose there are two tasks A and B such that the task A can be done in m different ways and task B can be completed in n ways. Then the number of ways to complete either of the two tasks is given by: (m + n) ways.

Calculation:

Given: 

Ram can travel from Delhi to Mumbai either by 2 different trains or by 3 different buses or by 1 plane.

So, the number of ways in which he can travel from Delhi to Mumbai

 = 2 + 3 + 1 = 6 ways.

Ram can travel from Mumbai to Andaman by two different planes.

So, the number of ways in which he can travel from Mumbai to Andaman = 2 ways.

So, number of ways in which he can reach Andaman from Delhi via Mumbai = (6 × 2) ways = 12 ways.

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