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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma

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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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New post 15 Mar 2015, 23:20
4
4
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A
B
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D
E

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  35% (medium)

Question Stats:

68% (01:26) correct 32% (02:06) wrong based on 101 sessions

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A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf?

(A) 720
(B) 1,512
(C) 2,520
(D) 6,400
(E) 12,600

Kudos for a correct solution.

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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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New post 16 Mar 2015, 00:23
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Hi
this is a simple arrangement question
plz see the description in the pic attached
Attachments

pp.png
pp.png [ 9.99 KiB | Viewed 1747 times ]


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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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New post 16 Mar 2015, 01:18
1
Bunuel wrote:
A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf?

(A) 720
(B) 1,512
(C) 2,520
(D) 6,400
(E) 12,600

Kudos for a correct solution.



easy one .

\(10!/4!3! 2! = 12600\)
Answer : E
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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New post 23 Mar 2015, 03:37
Bunuel wrote:
A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf?

(A) 720
(B) 1,512
(C) 2,520
(D) 6,400
(E) 12,600

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

If the ten books were all different, the arrangements would be (10!), a very big number. Because we have repeats of identical copies, not all 10! arrangements will be unique. For a subset of k identical members, those k members could be interchanged in k! orders, and the resulting arrangements would be the same, so we have to divide by k! to remove repetitions. In this example, we need to divide 10! by 4! and 3! and 2!:
Attachment:
1.png
1.png [ 42.21 KiB | Viewed 1643 times ]


Answer = (E)
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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New post 26 Feb 2017, 12:14
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma &nbs [#permalink] 26 Feb 2017, 12:14
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