How many ways can 11 boys on a soccer team be grouped into 4 forwards, 3 midfiel
ID: 3068880 • Letter: H
Question
How many ways can 11 boys on a soccer team be grouped into 4 forwards, 3 midfielders, 3 defenders, and 1 goalie? Additionally, suppose the coach assigns roles completely at random. Rudi, Georg and Alex are three of the team members. Find the following:
(a) The chance that Rudi, Georg and Alex are each a forward.
(b) The chance that one of Rudi, Georg or Alex is the goalie.
(c) The chance that Rudi is the goalie and Georg and Alex are forwards.
(d) The chance that one of the three is the goalie and the other two are forwards.
Explanation / Answer
Number of ways in which the teams can be formd = 11C4 x 7C3 x 4C3 x 1
= 330 x 35 x 4 x 1
= 46,200
a) P(Judi, Gorg and Alex are each forward) = 3/11 x 2/10 x 1/9
= 1/165
b) P(one of Rudi, Georg or Alex is the goalie) = 3/11
c) P(Rudi is the goalie and Georg and Alex are forwards) = 1/11 x 2/10 x 1/9
= 1/495
d) P(one of the three is the goalie and the other two are forwards) = 3/11 x 2/10 x 1/9
= 1/165
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