Question 1158823
A group of six friends consisting of 4 females and two males are seated in a
row. How many different seating arrangements are possible
     (A) If there is no restrictions of seating order?<pre>

         6! = 720</pre>

     (B) If all four females sit together.<pre> 

         There these 3 ways to choose them gender-wise:

         (WWWW)MM, M(WWWW)M, MM(WWWW)

For each of those 3 gender-wise choices,
There are 4 choices for the left-most female.
There are 3 choices for the next-to-left-most female.
There are 2 choices for the next-to-right-most female.
There is only 1 choice for the right-most female.
There are 2 choices for the left-most male.
There is only 1 choice for the right-most male.
          
Answer 3∙4∙3∙2∙1∙2∙1 = 144 ways</pre>

     (C) If the order is MWWMWW?<pre>

There are 4 choices for the left-most female.
There are 3 choices for the next-to-left-most female.
There are 2 choices for the next-to-right-most female.
There is only 1 choice for the right-most female.
There are 2 choices for the left-most male.
There is only 1 choice for the right-most male.

Answer 4∙3∙2∙1∙2∙1 = 48 ways</pre>

Edwin</pre>