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- There are 20 books of which 4 are single volume and the other are books of 8, 2 and 6 volumes respectively.
Question 1:
There are 20 books of which 4 are single volume and the other are books of 8, 2 and 6 volumes respectively. In how many ways can all these books be arranged on a shelf so that volumes of the same book are not separated? A. 2!3!4!5!
B. 3!4!5!6!
C. 4!5!6!7!
D. 8! 7! 6! 2!
Feedback Here volumes of the same book are not to be separated i.e. all the volumes of the same book are to be kept together. Regarding all volumes of the same book as one book, we have only 4 + 1 + 1 + 1 = 7 books. These 7 books can be arranged in 7! ways. Volumes of book having 6 volumes can be arranged in 6! ways. Volumes of book having 8 volumes can be arranged in 8! ways.
Volumes of book having 2 volumes can be arranged in 2! ways.
∴ Required number = 7! 8! 6! 2!.
Volumes of book having 2 volumes can be arranged in 2! ways.
∴ Required number = 7! 8! 6! 2!.
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