. The statistics department at the authors’ university participates in an annual volleyball tournament. Suppose that all 16 department members are willing to play. (a) How many different six-person...

. The statistics department at the authors’ university participates in an annual volleyball tournament.

Suppose that all 16 department members are willing to play.

(a) How many different six-person volleyball rosters could be generated? (That is, how many

years could the department participate in the tournament without repeating the same

six-person team?)

(b) The statistics department faculty consist of 5 women and 11 men. How many rosters

comprising exactly 2 women and 4 men can be generated?

(c) The tournament’s rules actually require that each team include at least two women. Under

this rule, how many valid teams could be generated?

(d) Suppose this year the department decides to randomly select its six players. What is the

probability the randomly selected team has exactly two women? At least two women?