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?
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            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 ?



<pre>
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


    {{{12!/(4!*5!*3!)}}} = {{{(1*2*3*4*5*6*7*8*9*10*11*12)/(24*120*6)}}} = 27720.


<U>ANSWER</U>.  The number of distinguishable arrangements is 27720.
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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.