Question

In a cinema hall, there are three entrance doors and two exit doors. In how many ways can a person enter the hall and then come out?

Answer 1

Hint: We will select 1 door from 3 entrance doors and we can select any of the doors. Hence 3 ways will be there to select an entry door. Similarly we will select 1 door from 2 exit doors and we can select any of the doors. Hence 2 ways will be there to select an exit door.

Complete step-by-step answer:
Here the person has to perform two operations as mentioned in the question. First operation is to enter the cinema hall from 1 door out of 3 entrance doors and second operation is to exit from the cinema hall from 1 door out of 2 exit doors.
Now the first operation can be done in 3 ways as there is no restriction and similarly the second operation can be done in 2 ways as there is again no restriction.
So from the fundamental principle of multiplication,
the required number of ways $=3\times 2=6$.
Hence, the teacher can make the selection of 1 entrance door and 1 exit door in 6 ways.

Note: Students can make a mistake in finding the total number of ways to select 1 entrance door and 1 exit door by adding all the ways and doing this they will get the answer as 5, hence remembering the concept of fundamental principle of multiplication is the key here. The fundamental counting principle (also called the multiplication rule) is a way to figure out the number of outcomes in a probability problem. Basically, we multiply the events together to get the total number of outcomes.