Problem preview

S-CP.9 Warmup M2-071-A04-V04

Use permutations and combinations to compute probabilities of compound events and solve problems.

Decide whether a counting situation uses a permutation or a combination

Problem

Decide whether assigning president, vice president, and secretary from \(12\) members is ordered by testing whether swapping \(\text{two}\) people changes the outcome. Name and justify the counting method.

Answer choices

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Use a permutation because president, vice president, and secretary are different offices, so switching people changes the outcome.

Use a combination because you are just choosing 3 club members, and the same 3 people count the same in any order.

Use a permutation because any time more than one person is chosen, every possible order should always be counted.

Use a combination because there are 12 club members total, so only which 3 are chosen matters, not who gets each office.

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Curriculum context

Course: Math II
Standard: S-CP.9
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Use permutations and combinations to compute probabilities of compound events and solve problems.
Problem type: Decide whether a counting situation uses a permutation or a combination