Question

Suraj wants to go to Delhi. He can choose from bus services or train services to downtown Punjab. From there, he can choose from 4 bus services or 7 train services to head to Delhi. The number of ways to get to Delhi is?

(a) 51

(b) 340

(c) 121

(d) 178

The question was asked during an internship interview.

The doubt is from Multiplication Theorem on Probability topic in portion Discrete Probability of Discrete Mathematics

Answer 1

Right choice is (c) 121

Explanation: Since Suraj can either take a bus or a train downtown and he has 4+7=11 ways to head downtown (Rule of sum). After that, he can either take a bus or a train to Delhi and hence he has another 4 * 7 = 11 ways to head to Delhi(Rule of sum). Thus, he has 11 * 11 = 121 ways to head from home to Delhi(Rule of product).