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Roger wants to arrange three of his five books on his bookshelf. Two o

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Director
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Status: It's near - I can see.
Joined: 13 Apr 2013
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Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
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Roger wants to arrange three of his five books on his bookshelf. Two o [#permalink]

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New post 13 May 2018, 11:01
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Difficulty:

  55% (hard)

Question Stats:

37% (01:51) correct 63% (01:23) wrong based on 35 sessions

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Roger wants to arrange three of his five books on his bookshelf. Two of the five books are duplicates and can not both be selected. In how many different ways can Roger arrange his books?

1. 12
2. 36
3. 42
4. 60
5. 128

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Location: India
Concentration: Entrepreneurship, Operations
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GMAT 2: 640 Q47 V31
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Re: Roger wants to arrange three of his five books on his bookshelf. Two o [#permalink]

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New post 13 May 2018, 16:15
QZ wrote:
Roger wants to arrange three of his five books on his bookshelf. Two of the five books are duplicates and can not both be selected. In how many different ways can Roger arrange his books?

1. 12
2. 36
3. 42
4. 60
5. 128


Case 01 : when none of the duplicates are selected.
3 books remained(As 2 of the 5 are duplicates).
Hence, the number of ways 3 books can be selected from 3 is 3C3=1

Case 02: when one of the duplicates are selected.
Total number of ways
=The number of selections of the books that are completely diff from each other and the duplicate ones * The number of selections of the duplicate books
=The number of ways 2 books can be selected from 3 * The number of ways 1 books can be selected from 2
=3C2 * 2C1
= 3*2
= 6
Hence, total number of selection of 3 books = Case 01 selections + Case 02 selections = 6+1=7

Now 3 books can be arranged on 3P3 ways among themselves. i.e., 3! ways= 6 ways

Hence , the total number of arrangements = 7*6 = 42 ..... Thus I would go for option C.
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Re: Roger wants to arrange three of his five books on his bookshelf. Two o   [#permalink] 13 May 2018, 16:15
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Roger wants to arrange three of his five books on his bookshelf. Two o

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