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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?

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Anzanzio

Answer:

The number of distinct arrangements is 12600.

Step-by-step explanation:

This is a permutation type of question and therefore the number of distinguishable permutations is:

n!/(n₁! n₂! n₃! ... nₓ!)

where

  • n₁, n₂, n₃ ... is the number of arrangements for each object
  • n is the number of objects
  • nₓ is the number of arrangements for the last object

In this case

  • n₁ is the identical copies of Hamlet
  • n₂ is the identical copies of Macbeth
  • n₃ is the identical copies of Romeo and Juliet
  • nₓ = n₄ is the one copy of Midsummer's Night Dream

Therefore,

Number of distinct arrangements =  10!/(4! × 3! × 2! × 1!)

                                                        = 12600 ways

Thus, the number of distinct arrangements is 12600.

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