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

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Bunuel
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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma [#permalink] New post   15 Mar 2015, 23:20
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72% (01:54) correct 28% (02:21) wrong based on 276 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

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E
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma [#permalink] 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
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Lucky2783
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma [#permalink] New post   16 Mar 2015, 01:18
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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

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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] New post   23 Mar 2015, 03:37
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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 7934 times ]


Answer = (E)
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma [#permalink] New post   25 May 2020, 11:55
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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



We use the indistinguishable permutations formula, wherein the normal number of permutations (numerator) is divided by the product of the factorial(s) of the number(s) of indistinguishable items in each set. Thus, the number of distinct arrangements is:

10! / (4! x 3! x 2! x 1!) = (10 x 9 x 8 x 7 x 6 x 5) / (3 x 2 x 2) = 5 x 3 x 4 x 7 x 6 x 5 = 12,600

Answer: E
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma [#permalink]
25 May 2020, 11:55
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