A club meets 9 times per year. Club has 18 people, 11 women and 7 men. How many outcomes where women preside exactly 6 times?

Question

An Anarchists’ Club meets 9 times per year. The club has 18 members including 11 women and 7 men. At each meeting one person is selected to preside, but no one can preside at more than one meeting in the course of a year. If a record is kept of who presided at each meeting during one year, in how many possible overall outcomes would women preside exactly 6 times?

Answer 1

Shawn, this is the Product of the ways six women being chosen out of 11 and the ways the remaining three 

Presiding persons are men out of a Possible 7 men. Or:

11!/6!5! Times 7!/3!4!

 

Hope that helps,

Deanna