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A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo...

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by AAPL » Tue May 19, 2020 1:16 pm

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Magoosh

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

OA E
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Re: A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo...

by Scott@TargetTestPrep » Sun May 24, 2020 6:05 am
AAPL wrote: ↑
Tue May 19, 2020 1:16 pm
 Magoosh

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

OA E
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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