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10 Feb 2021, 09:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
18% (01:46) correct
82%
(01:43)
wrong
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A shelf contains 20 different books of which 4 are in single volume and the others form sets of 8, 5 and 3 volumes respectively. Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order is
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
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10 Feb 2021, 23:07
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Bunuel
So what do we have in 20 books : \(A, B, C, D, (E_1, E_2...E_8), (F_1, F_2....F_5), (G_1, G_2, G_3)\)
Now, as all the volumes of a book are together and in due order, we can take \((E_1, E_2...E_8), (F_1, F_2....F_5), (G_1, G_2, G_3)\) as \(E_{(1-8)}, \ \ F_{(1-5)} \ \ G_{(1-3)}\)
Thus we have 7 books : \(A, B, C, D, E_{(1-8)}, \ \ F_{(1-5)} \ \ G_{(1-3)}\). These can be arranged in 7! ways.
Now, due order could mean ascending order or descending order, that is it could be \(E_{(1-8)}, \ \ or \ \ E_{(8-1)}\), so each of sets of E, F and G can be arranged in 2 ways each.
Answer = 7!*2*2*2=8*7!=8!
C
17 Apr 2022, 09:31
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Bunuel
The problem with the question is that the phrase "in their due order" is just not something anyone says in English, so there's no way to guess what it means. I imagine Chetan above has guessed the question designer's intention, but I've never seen a set of books arranged "in order" where the books went, from left to right, Volume 3, Volume 2, then Volume 1. I would assume here that the sets of books are arranged Volume 1, Volume 2, and Volume 3 from left to right. And if that's what we're doing, we really just have seven books (four individual books, and three sets that are in a fixed order) and the answer is 7!.
If the question means something else, it needs to be worded differently, because there's no way to guess the answer should be 8! here.
