6.6 Worksheet Exercise 6.6.1: Selecting students for jobs. (a) A teacher selects 4 students from her class of 37 to work together on a project. How many ways are there for her to select the students? (b)A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick up homework, hand out permission slips, staple worksheets, and organize the classroom library. Each job is performed by exactly one student in the class and no student can get more than one job. How many ways are there for her to select students and assign them to the jobs? Exercise 6.6.2: Results of a piano competition. 120 pianists compete in a piano competition. (a) In the first round, 30 of the 120 are selected to go on to the next round. How many different outcomes are there for the first round? word Owynom (b) In the second round, the judges select the first, second, third, fourth and fifth place winners of the competition from among the 30 pianists who advanced to the second round. How many outcomes are there for the second round of the competition? 26 GAGH2 Exercise 6.6.3: Choosing a lineup for a traveling basketball team. There are 20 members of a basketball team. (a) The coach must select 12 players to travel to an away game. How many ways are there to select the players who will travel? Page 1 of 3 6.6 Worksheet (b) From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, power forward, small forward, shooting guard and point guard. How many ways are there for her to select the starting line-up? (b) : par orc (c) From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, power forward, small forward, shooting guard and point guard. However, there are only three of the 12 players who can play center. Otherwise, there are no restrictions. How many ways are there for her to select the starting line-up? Exercise 6.6.4: Hiring a software engineer. A search committee is formed to find a new software engineer. (a)lf 100 applicants apply for the job, how many ways are there to select a subset of 9 for a short list? (b) If 6 of the 9 are selected for an interview, how many ways are there to pick the set of people who are interviewed? (You can assume that the short list is already decided). 29gbul (d) (c) Based on the interview, the committee will rank the top three candidates and submit the list to their boss who will make the final decision. (You can assume that the interviewees are already decided.) How many ways are there to select the list from the 6 interviewees? 812001) Exercise 6.6.5: Counting orders at a restaurant. A group of five friends go to a restaurant for dinner. The restaurant offers 20 different main dishes. a) Suppose that the group collectively orders five different dishes to share. The waiter just needs to place all ve dishes in the center of the table. How many different possible orders are there for the group? Page 2 of 3