Question

A student employee at ULS has been asked by the Library Director to arrange 12 books (6 Finance, 4 Accounting, and 2 Marketing) on a shelf in a certain section of the library.

1. Determine the number of ways of arranging the books on the shelf if no restrictions are in place; that is, the books can be anywhere on the shelf.

2. Determine the number of ways of arranging the books on the shelf, such that each category stays together.

3. Determine the number of ways of arranging the books on the shelf, such that only the Finance books stay together.

4. Determine the number of ways of arranging the books on the shelf, such that each category stays together in the following order: Finance, Accounting, and Marketing.

Answer 1

Question

1. Here number of ways of arranging the books on the shelf if no restrictions are in place; that is, the books can be anywhere on the shelf = 12!

as there are 12 place and 12 books to arrange

2. number of ways of arranging the books on the shelf, such that each category stays together.

= 3! 6! 4! 2!  

as there are 6! ways to arrange finance books, 4! to arrange accounting books and 2! to arrange marketing books.

and 3! for arranging all 3 categories books.

3. number of ways of arranging the books on the shelf, such that only the Finance books stay together. = 6!7! - 6!4!2! 3!

as we group all finance books together and then there would be 7 books and there are 7! combinations.and 6! forinternal finance books. Now 6!4!2!3! when they aare in order.

4. number of ways of arranging the books on the shelf, such that each category stays together in the following order: Finance, Accounting, and Marketing.= 6! 4! 2!

there is fixed order.

4.