Group of 10 men and 10 women.

Only 8 seats availableThere are C(20,8) total possible arrangements. The best way to find at least 1 woman sitting is to find the number with no woman sitting and subtract from the total. With no woman sitting is C(10,8), only the men.How many arrangements if at least one woman should sit?

Tie Mary and Gail together and pretend they are one big person. Count the number of arrangements that way and subtract from the total number of ways.Mary and Gail should both sit, but not beside each other?