Question 1114136
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<pre>
(I)  It is VERY STANDARD introductory problem on PERMUTATIONS for beginners.


     The answer is  7! = 1*2*3*4*5*6*7.


     The standard solution (=mantra) is this:


         You can put any of the 7 books in the 1-st position in 7 ways.

         You can put any of the remaining 6 books in the 2-nd position in 6 ways.
         
         You can put any of the remaining 5 books in the 3-rd position in 5 ways.


         . . . and so on . . . 


         You can put any of the remaining 2 books in the 6-th position in 2 ways.


         Finally, you can put the last remaining 1 book in the 7-th position in 1 way only (there is nothing to select from at this step . . . ).

         
         Since these selections/options are independent, you have  7! = 7*6*5*4*3*2*1  ways, in all.
</pre>

Solved.


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On Permutations, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Problems on Permutations</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</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 lessons are 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.