Question 1113347
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I do not understand why other tutor has some/any doubts.


There is one and only one reasonable way to read/(to interpret) the condition: " . . . such that NO two boys are sitting together".



<pre>
In this problem, you can assume that all the "seats" are numbered from 1 to 10, from left to right. 


Then, under given conditions, there are only TWO major configurations:


    a)  the boys are placed at the "odd" seats;   and/or

    b)  the boys are placed at the "even" seats.


Case a) gives  5! = 120 different arrangements for boys and the same number of 5! = 120 different arrangements for girls.

In all, there are  {{{120^2}}}  arrangements, when the boys are seating at  "odd" seats.



Case b) gives  {{{120^2}}}  different arrangements, too (by the same arguments).


Hence, there are  {{{2*120^2}}}  arrangements, in all.
</pre>

Solved.


---------------
On permutations, 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.