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?

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.