Probabilities

1. In a bicycle race the are two teams: team Blue with 4 members and team Red with 2 members. There are no other teams. Employ an alphabet to determine the sample space of all possible rankings for the first three ranks and to compute the probability that (at the same time) one member of team Red will get the 1st rank of the race and at least one member of Team Blue is on one of the following two ranks. (We assume that each cyclist has the same chance to achieve the first three ranks).

2. During the summer Olympic games, in a teams sports program, take part 29 countries (for each state there is an exact team), including Australia, Belgium, and Chile. Employ combinatorics to answer the following questions: How many rankings of the best 9 teams exist? What is the probability that at least one of the three countries Australia, Belgium, and Chile is on the ranking list of the best 9 teams?