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10 Nov 2022, 07:54
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
36% (01:40) correct
64%
(01:46)
wrong
based on 106
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40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
A. \(17!*14!*3!\)
B. \(17!*14!*9!\)
C. \(17!*14!*9!*39\)
D. \(\frac{40!}{9!}\)
E. \(32!\)
A. \(17!*14!*3!\)
B. \(17!*14!*9!\)
C. \(17!*14!*9!*39\)
D. \(\frac{40!}{9!}\)
E. \(32!\)
10 Nov 2022, 09:25
Kudos
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So we have three sets of DVDs - psychology, biology and history. These DVDs can be arranged in any order, except 9 history-related DVDs are, on the whole, needs to be arranged in chronological order.
In total we have 40 DVD , these DVDs can be arranged in 40! ways.
Now note, that in this arrangement we have considered all possible arrangements of the history related DVDs as well. However, only one arrangement is possible for the history related DVDs. Hence we need to un-arrange them. Hence the 9! ways in which the DVDs could have been arranged needs to be factored out.
Total number of ways = \(\frac{40! }{ 9!}\)
IMO D
In total we have 40 DVD , these DVDs can be arranged in 40! ways.
Now note, that in this arrangement we have considered all possible arrangements of the history related DVDs as well. However, only one arrangement is possible for the history related DVDs. Hence we need to un-arrange them. Hence the 9! ways in which the DVDs could have been arranged needs to be factored out.
Total number of ways = \(\frac{40! }{ 9!}\)
IMO D
19 Nov 2022, 06:46
Kudos
Bookmarks
But the 9 history-related DVDs are, on the whole, arranged in chronological order. So they can be considered as a single DVD. And thereby the total ways could be 32!. Why are the arrangement of 9 DVDs getting divided? Shouldn't division be done when the objects are identical?
