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

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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15 Mar 2015, 22:20
4
6
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:45) correct 33% (02:23) wrong based on 141 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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15 Mar 2015, 23:23
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1
Hi
this is a simple arrangement question
plz see the description in the pic attached
Attachments

pp.png [ 9.99 KiB | Viewed 2216 times ]

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Joined: 07 Aug 2011
Posts: 536
GMAT 1: 630 Q49 V27
Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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16 Mar 2015, 00:18
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 .

$$10!/4!3! 2! = 12600$$
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Joined: 02 Sep 2009
Posts: 51280
Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma  [#permalink]

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23 Mar 2015, 02:37
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 [ 42.21 KiB | Viewed 2112 times ]

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

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30 Sep 2018, 09:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma &nbs [#permalink] 30 Sep 2018, 09:36
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