Provide solutions in the form "P(n, r)" or "n choose r" (e.g. P(8, 3) or 8 choose 3).
1) Dave swims three times in the week. How many ways are there to plan his workout schedule (i.e. which days he will swim) for a given week?
7 choose 3
Correct
7 choose 3
A schedule for Dave's workouts consists of the set of three days he will swim (e.g., {Mon, Wed, Sat}). The order in which he selects the three days of the week does not affect the schedule.
Therefore, Dave is selecting a subset of 3 days from the 7 days of the week.
2) Dave will swim one day, run one day, and bike another day in a week. He does at most one activity on any particular day. How many ways are there for him to select his workout schedule (i.e. which activities he does which days)?
Incorrect
A sample schedule would be that Dave swims Saturday, runs on Monday, and bikes on Wednesday. A different schedule is that Dave bikes Monday, runs Wednesday, and bikes Saturday.
3) The students in a class elect a president, vice president, secretary, and treasurer. There are 30 students in the class and no student can have more than one job. How many different outcomes are there from the election process?
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4) A class of 30 students elects four students to serve on a student leadership council. The teacher tallies the votes and only reveals the names of the four students who received the most votes. How many different outcomes are there from the election process?
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