)in how many ways can 5 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order?40320 (b) the mathematics books must be together and the novels must be together?(c) the mathematics books must be together but the other books can be arranged in any order?

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