Alibrarian 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 objectn is the number of objectsnₓ is the number of arrangements for the last object

In this case

n₁ is the identical copies of Hamletn₂ is the identical copies of Macbethn₃ is the identical copies of Romeo and Julietnₓ = 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.

I'm sorry, I'd love to answer your question, but there is no graph.  If you still want an answer, you need to take a picture and send it to the question.  Then I can answer it.  If you can't, you can just tell me two of the points and I will find the slope.  Thanks :)