SOLUTION: How many ways can a 2 Physics books, 4 Mathematics books and 3 Chemistry books be arranged on a shelf if all books of the same subject may be arranged in any order but must be toge

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Question 1179169: How many ways can a 2 Physics books, 4 Mathematics books and 3 Chemistry books be arranged on a shelf if all books of the same subject may be arranged in any order but must be together?
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

There are 2! =  2 permutations inside the block of 2 Physics books;

          4! = 24 permutations inside the block of 2 Math books;  and

          3! =  6 permutations inside the block of 3 Chemistry books.


Also, there are 3! = 6 permutations of these 3 blocks as whole items.


THEREFORE, the are  2*24*6*6 = 1728 different permutations under the posed conditions, in all.

Solved, answered, explained and completed.

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

On permutations, see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems
    - Problems on Permutations with restrictions
    - Fundamental counting principle problems
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 lessons are 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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Do not forget to post your  "THANKS"  for my teaching.



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