Question

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?

Answer 1

The number of distinct arrangements is 12600.

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.