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Combinations : Application Word Problems (5 Problems)

2. A group pf 12 students have been hired by the city this summer to work as ground keepers.
(a) During their first week of employment, half will be assigned to pick up garbage down town while the other half go on a training course. The second week, they will switch places. In how many distinct ways can 12 students be assigned to training sessions (I.e., Week 1 or Week 2)?
(b) Once all of the students have had their training, they will be assigned to 3 teams with 4 workers on each team and team duties will be assigned.
(i) If each team is assigned to a different duty ( grass cutting, flower planting or tree trimming) and all of these teams will be assigned to the same one of four city parks, in how many distinct ways can the assignments (of teams and duties) be made?
(ii) If, instead, all 3 teams will be assigned to the same one of the 3 duties, but each team is assigned to a different one of the 4 parks, in how many distinct ways can the assignments be made

(c) After a big storm, which knocked down many trees within the city, the students are temporarily re-assigned to fallen tree disposal clean-up duty along the river. The 12 students will be divided in 4 teams of 3. Within each team, one person will use a power saw, one will use a hatchet to trim smaller branches and the third will bag the trimmings and chase away any children who come along. Each team will start from the same place and wander along the river until they find a tree which needs disposal. In how many distinct ways can the students be divided into the teams and the duties within the teams assigned?

Solution Preview

2.A group pf 12 students have been hired by the city this summer to work as ground keepers.
(a) During their first week of employment, half will be assigned to pick up garbage down town while the other half go on a training course. The second week, they will switch places. In how many distinct ways can 12 students be assigned to training sessions (I.e., Week 1 or Week 2)?

We need to choose 6 students to be assigned to the first group; that is, 12 choose 6, or 12! / (6! * 6!) = 924 different ways.

(b) Once all of the students have had their training, they will be assigned to 3 teams with 4 workers on each team and team duties will be assigned.
(i) If each team is assigned to a different duty ( grass cutting, ...

Solution Summary

Five combination problems are solved. The solution is detailed and well presented.

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