Answer:
a. 40320
b. 1440
c. 10080
Step-by-step explanation:
Number of Novels: 5
Numbers of Mathematics books: 2
Number of biology: 1
a. If the books are to be arranged in any order
Total number of books = 5 + 2 + 1 = 8
Number of Arrangements = 8!
Number of Arrangements = 8*7*6*5*4*3*2*1
Number of Arrangements = 40320 ways
b. The mathematics books must be together and the novels must be together
To get the number of possible arrangements
First, Calculate the Possible Arrangements of Mathematics Books;
Number of Mathematics Books = 2
Arrangements = 2!
Arrangements = 2*1 = 2
Then, Calculate the Possible Arrangements of Novel Books;
Number of Novel Books = 5
Arrangements = 5!
Arrangements = 5*4*3*2*1
Arrangements = 120
Then Calculate the Possible Arrangements of the Mathematics book bundle, Novel Bundle with Biology book.
The mathematics book bundled together is 1
The novel bundled together is 1
Other books = 1 Biology
Total = 3
Arrangements = 3!
Arrangements = 3*2*1 = 6
Total Arrangements = 2 * 120 * 6
Total Arrangements = 1440
c. If the mathematics book must be together but other books can be arranged in any order
To get the Number of Possible Arrangements
First, Calculate the Possible Arrangements of Mathematics Books;
Number of Mathematics Books = 2
Arrangements = 2!
Arrangements = 2*1 = 2
Then Calculate the Possible Arrangements of the Mathematics book bundle with other books;
The mathematics book bundled together is 1
Other books = 5 Novels + 1 Biology
Total = 7
Arrangements = 7!
Arrangements = 7*6*5*4*3*2*1
Arrangements = 5040
Total Possible Arrangements = 2 * 5040 = 10080 ways
