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12 Apr 2025, 03:56
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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:
45%
(medium)
Question Stats:
74% (02:16) correct
26%
(02:35)
wrong
based on 235
sessions
History
Date
Time
Result
Not Attempted Yet
From a shelf of 12 books arranged by height, a librarian will select a set of 4 books to be featured in a display. If the librarian will not choose a set of 4 books that are next to each other on the shelf, how many different sets of 4 books could be chosen by the librarian?
A. 480
B. 483
C. 486
D. 491
E. 495
A. 480
B. 483
C. 486
D. 491
E. 495
12 Apr 2025, 05:06
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This is actually an easy question.
Maybe 600-645 level to be honest
There are 12C4 ways of choosing 4 books
Now, the question says that we need to choose books that are not next to each other. We can negate that and calculate the number of ways we can choose books that are next to each other
1->4, 2->5, 3->6 .............. 9->12 -> 9 ways
12C4 = 495
Answer is 495-9 = 486
Maybe 600-645 level to be honest
There are 12C4 ways of choosing 4 books
Now, the question says that we need to choose books that are not next to each other. We can negate that and calculate the number of ways we can choose books that are next to each other
1->4, 2->5, 3->6 .............. 9->12 -> 9 ways
12C4 = 495
Answer is 495-9 = 486
General Discussion
13 Apr 2025, 00:39
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saynchalk
Total Sets of 4 books out of 12 - 12C4 = 495
1 2 3 4 5 6 7 8 9 10 11 12
Undesired Sets = {1 2 3 4}| {2 3 4 5} | {3 4 5 6} | {4 5 6 7} | {5 6 7 8} | {6 7 8 9} | ........ {9 10 11 12} = 9 Sets
Favorable outcomes = 495 - 9 = 486
Answer: Option C
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