Question 1160504
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            It is strange to me to see placed into one capsule three totally different in their complexity subjects.


            Part  (a)  is trivial and routine;


            Part  (b)  is trivial and routine,  too;


            and finally part  (c)  is of the totally different level of complexity.


            I will answer part  (c),  ONLY.



<pre>
Imagine that the 8 women are standing in line with intervals (gaps) between them, as shown in the Figure below.


                     * W * W * W * W * W * W * W * W *


(" * "s  show intervals, or gaps). You see 7 stars between "W"s and two stars before and after the W-line; in all, 7+2 = 9 stars.

These stars are the only places for men: Each man can occupy one and only one position at the star place.


So, we can position 8 women by 8! = 8*7*6*5*4*3*2*1 = 40320 ways.


And we can place first  man in any of nine (*)-positions;

                 second man in any of remaining eight (*)-positions;

                 third  man in any of remaining seven positions;

                 fourth . . . 

             and fifth . . . 


Thus, in all, there are  8!*9*8*7*6*5 = 40320*9*8*7*6*5 = 609638400 differennt arrangements satisfying given restrictions.    <U>ANSWER</U>
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Solved.