Your literature class will read 4 novels this year, chosen by class vote from a list of 7 possible books offered by the teacher. a) How many different ways could the course unfold, given that it probably matters what order you read the books in?
b) How many different choices of books could the class make?
a) The number of different ways the course could unfold is

a) 840 different ways

b) 35 different choices of books

Step-by-step explanation:

We know that our literature class will read a total of 4 novels this year.

All novels chosen by class vote from a list of 7 possible books offered by the teacher.

Wherever we have an experiment which is formed by sub - experiments that can occurred in ways, the total number of ways in which the whole experiment can be developed is :

x x ... x

Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :

(I)

Because for the first book there are 7 different choices. Now, given that we choose the first book, we only have 6 different choices for the second one.

Continuing with the idea, we deduce the equation (I).

For item b) :

Wherever we have different objects and we want to find the ways that we can choose objects from that group, we need to use the combinatorial number.

We define the combinatorial number as :

Then, if we apply this to the problem, the total different choices of books if we want 4 novels voting from a total of 7 possible books is :

a) 840 different ways

b) 35 different choices of books