SOLUTION: Finite mathematics: 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

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Question 1158823: Finite mathematics:
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?
(B) If all four females sit together.
(C) If the oder is MWWMWW?
Found 2 solutions by Edwin McCravy, somuahkata@gmail.com:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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?

         6! = 720

(B) If all four females sit together.
 

         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

(C) If the order is MWWMWW?

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

Edwin
Answer by somuahkata@gmail.com(7)   (Show Source): You can put this solution on YOUR website!
.
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