Problem 4

(a) How many ways can 11 boys on a soccer team be grouped into 4 forwards, 3 midelders, 3 defenders

and 1 goalie?

Additionally, suppose the coach assigns the roles completely at random. Rudi, George and Alex are three of

the team members. Find the following:

(b) The probability that Rudi, George and Alex are each a forward.

(c) The probability that one of Rudi, George or Alex is the goalie.

(d) The probability that Rudi is the goalie, and George and Alex are forwards.

(e) The probability that one of the three is the goalie, and the other two are forwards.