From Goa to Bombay there are two routes; air, and sea. From Bombay to Delhi there are three routes; air, rail, and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
From Goa to Bombay there are two routes; air, and sea. From Bombay to Delhi there are three routes; air, rail, and road. From Goa to Delhi via Bombay, how many kinds of routes are there?

Solution:

According to the question, there are two routes from Goa to Bombay which is air and sea. So, the number of ways in which a person can travel from Goa to Bombay is given by 2C1

According to the question, there are three routes from Bombay to Delhi: air, rail, and road. So, the number of ways in which a person can travel from Bombay to Delhi is given by 3C1

Therefore, the number of ways in which a person can travel from Goa to Delhi via Bombay is given by:

2C1 × 3C= 2 × 3

2C1 × 3C1 = 6 ways.