SOLUTION: 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 item

Question 1044374: 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?
18
36
72
216
432
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
There are 3 novels, 2 SG, and 3 textbooks.
They can be grouped 6 ways
N,S,T
N,T,S
S,T,N
S,N,T
T,S,N
T,N,S
Wishing each grouping, the novels can be grouped 6 ways, 3 ways to choose the first*2 for the second*1 for the third.
The SG can be grouped two ways
The textbooks can be grouped 6 ways.
These are multiplied to get 6*2*6=72.
The combined product of the two, groups of books and within each group is 72*6=432.

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