Final answer:
To seat 5 men and 4 women in a row so that the women occupy the even places, there are 2,880 possible arrangements.
Step-by-step explanation:
To seat 5 men and 4 women in a row so that the women occupy the even places, we can start by considering the even places in the row. There are 5 even places in total. Since there are 4 women to be seated in these even places, we can choose the 4 places for the women in
4 imes 3 imes 2 imes 1 = 24
ways. Now, we have 5 remaining places for the men. The men can be seated in these remaining places in 5! (5 factorial) ways. Therefore, the total number of arrangements is
24 imes 5! = 24 imes 5 imes 4 imes 3 imes 2 imes 1 = 2,880.