The number of ways of the books can be arranged are illustrations of permutations.
- When the books are arranged in any order, the number of arrangements is 3628800
- When the mathematics book must not be together, the number of arrangements is 2903040
- When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
- When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400
The given parameters are:
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<u>(a) The books in any order</u>
First, we calculate the total number of books
The number of arrangement is n!:
So, we have:
<u>(b) The mathematics book, not together</u>
There are 2 mathematics books.
If the mathematics books, must be together
The number of arrangements is:
Using the complement rule, we have:
This gives
<u>(c) The novels must be together and the chemistry books, together</u>
We have:
First, arrange the novels in:
Next, arrange the chemistry books in:
Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.
Literally, the number of books now is:
So, the number of arrangements is:
<u>(d) The mathematics must be together and the chemistry books, not together</u>
We have:
First, arrange the mathematics in:
Literally, the number of chemistry and mathematics now is:
So, the number of arrangements of these books is:
Now, there are 7 spaces between the chemistry and mathematics books.
For the 3 novels not to be together, the number of arrangement is:
So, the total arrangement is:
Read more about permutations at:
brainly.com/question/1216161