Answer:
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 [tex]''N''[/tex] which is formed by sub - experiments that can occurred in [tex]m_{1},m_{2},...,m_{n}[/tex] ways, the total number of ways in which the whole experiment [tex]''N''[/tex] can be developed is :
[tex]m_{1}[/tex] x [tex]m_{2}[/tex] x ... x [tex]m_{n}[/tex]
Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :
[tex](7).(6).(5).(4)=840[/tex] (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 [tex]''n''[/tex] different objects and we want to find the ways that we can choose [tex]''r''[/tex] objects from that group, we need to use the combinatorial number.
We define the combinatorial number as :
[tex]nCr=\left(\begin{array}{c}n&r\end{array}\right)=\frac{n!}{r!(n-r)!}[/tex]
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 :
[tex]7C4=\frac{7!}{4!(7-4)!}=35[/tex]
a) 840 different ways
b) 35 different choices of books
