Eight men and eight women have six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman and the people alternate woman, man, woman, man and so on?

As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is

W

M

W

M

W

M

in that order.

Now as we four women, three seats for women can be filled in

X

4

P

3

=

24

ways

and similarly as we four men, three seats for men can be filled in

X

4

P

3

=

24

ways

Hence, total

24

*

24

=

576

permutations.