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Bunuel
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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma 15 Mar 2015, 23:20
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E
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25% (medium)

Question Stats:

74% (01:55) correct 26% (02:15) wrong based on 343 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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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma 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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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma 16 Mar 2015, 01:18
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Bunuel
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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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma 23 Mar 2015, 03:37
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Bunuel
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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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 9597 times ]

Answer = (E)
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A librarian has 4 identical copies of Hamlet, 3 identical copies of Ma 25 May 2020, 11:55
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Bunuel
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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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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