exercise 33: use fundamental counting principle

34. out of a group of eight students serving on the student government association, how many different ways can a president, a vice president, and a treasurer be selected?

Question

exercise 33: use fundamental counting principle

34. out of a group of eight students serving on the student government association, how many different ways can a president, a vice president, and a treasurer be selected?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fundamental Counting Principle", "Permutations" ], "new_concepts": [], "current_concepts": [ "Fundamental Counting Principle", "Permutations" ] } ## Identify the selection stages and available choices $$ \begin{aligned} &\text{Total students } (n) = 8\ &\text{Positions to fill } (k) = 3 \quad (\text{President, Vice President, Treasurer}) \end{aligned} $$ ## Apply the Fundamental Counting Principle $$ \begin{aligned} &\text{Ways to choose President} = 8\ &\text{Ways to choose Vice President} = 7\ &\text{Ways to choose Treasurer} = 6 \end{aligned} $$ ## Calculate the total number of ways $$ \text{Total ways} = 8 \times 7 \times 6 = 336 $$ 336 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Fundamental Counting Principle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the selection stages and available choices

Apply the Fundamental Counting Principle

Calculate the total number of ways

Answer: