Video Explanation

Text Explanation

This is a question in which we have to count all possible ways to complete a process in phases. This means that we have to count the number of ways that each phase is done with and then, according to the Fundamental Principle of Counting, multiply them to find the total number of ways. 

In here, the process is assembling the reading list and this process is split into two phases: Selecting the 3 novels and selecting the 2 non-fiction books.

So, we need to count all the ways that we have to select 3 novels out of 5 and to select 2 non-fiction books out of 4.

As there are two formulas that we use in counting problems, the formula for permutations when we are interested about the order of the selected objects and the formula for combinations when we do not care about the order, we first need to determine if the order matters here.

Let’s think of the nature of the problem for a minute: We want to choose 3 novels out of 5 available and put them in the reading list. Do we care about their order that will be selected? Is there any special reason for one of them to be first, another one second and the last one third. No, we do not care about that. We just want the 3 novels to be in the reading list that we make, we do not care what is first, second, third, nor do we make any suggestions about the order that these should be read by the students. So, the order does not matter and thus we will use the combination formula. The same for the non-fiction books, we do not care about their order too.

So, for novels we use the formula for combinations:

For non-fiction books we have:

Therefore, the total number of ways to complete the reading list:

6 ⨉ 10 = 60