SOLUTION: There are 4 copies of Statistics book, 5 copies of Science book, and 3 copies of English book. In how many ways can they be arranged on a shelf?

Question 1185054: There are 4 copies of Statistics book, 5 copies of Science book, and 3 copies of English book. In how many ways can they be arranged on a shelf?
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
There are 4 copies of Statistics book, 5 copies of Science book,
and 3 copies of English book. In how many ways can they be arranged on a shelf?
~~~~~~~~~~~~~~~

            Based on context, I interpret the given part as if the copies of each kind are undistinguishable.

            Then the question is: how many DISTINGUISHABLE arrangements are there in this situation ?

The total number of books is  4+5+3 = 12;  the multiplicities are  4, 5 and 3.


Use the formula for the number of distinguishable arrangements and get the number


     =  = 27720.


ANSWER.  The number of distinguishable arrangements is 27720.

Solved.

----------------

To see many other similar (and different) solved problems, look into the lesson
- Arranging elements of sets containing indistinguishable elements
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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