Question 1152347
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<pre>

(a)  10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 ways.


     Any of 10 questions can be placed first;

     any of remaining 9 questions can be placed 2-nd;

     any of remaining 8 questions can be placed 3-rd

         . . . . and so on . . . . 



(b)  We can consider two special questions as one single object in 2 states, that are its internal permutations AB and BA.


    Then we have 9 objects and 9! their permutations with one the special object which has 2 states.


    Therefore, in all, there are  2*9! different ways = 725760 ways.



(c)  From the entire set of all possible permutations of 10 questions, subtract the number of (b) to get the answer


     10! - 2*9! = 725760 = 3628800 - 725760 = 2903040.
</pre>

Solved.  All questions are answered.


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This problem is about PERMUTATIONS.


On Permutations, &nbsp;see introductory 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.