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
(