The Northeastern University College of Computer and Information Science
has 5 women and 20 men who are full-time faculty members.
Their photos are to be displayed in a single row at the entrance to their building.
(iii) In how many ways can the photos be displayed so that no two women are adjacent?
Hint: Consider arranging the menís photos first and then placing the womenís photos
among the menís photos so as to ensure that no two women are adjacent.
That hint tells the whole story . . .
Place the 20 men's photos in a row. .There are ways.
Leave a space between the men's photos and on the ends.
. . _ M _ M _ M _ M _ ... _ M _ M _ M _
To place the women's photos, we choose 5 of the available 21 spaces.
. . There are: . ways.
Therefore, there are: . ways.