Question

A book store has received 8 different books, of which 3/8 are novels, 25% are study guides and remaining are textbooks. If all books must be placed on one shelf displaying new items and if books in the same category have to be shelved next to each other, how many different arrangements of books are possible?A. 18B. 36C. 72D. 216E. 432

Answer 1

E.432

Explanation:

We are given that

Total number of books=8

Novels=
`(3)/(8)* 8=3`

Study guides=25% of 8=
`(25)/(100)* 8=2`

Textbooks=8-(3+2)=3

We have to find the possible number of arrangements of books .

Number of ways in which novels can be arranged=3!
`=3* 2* 1=6`

Using formula:
`n!=n(n-1)(n-2)(n-3)....2* 1`

Number of ways in which study guides can be arranged=2!=
`2* 1=2`

Number of ways in which textbooks can be arranged=
`3!=3* 2* 1=6`

Number of category of books=3

Therefore, number of ways in which 3 types of books can be arranged=3!=6

Total possible number of arrangement of books=
`6* 2* 6* 6=432`

Option E is true