in how many ways can the first 4 guests arrive at a party if 15 guests have been invited?

\{}_{n}p_{r} = \frac{n!}{(n-r)!}\

Question

in how many ways can the first 4 guests arrive at a party if 15 guests have been invited?

\{}_{n}p_{r} = \frac{n!}{(n-r)!}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Permutations", "Factorial Notation" ], "new_concepts": [], "current_concepts": [ "Permutations", "Factorial Notation" ] } ## Identify the permutation parameters $$ \begin{aligned} n &= 15 \ r &= 4 \end{aligned} $$ ## Apply the permutation formula $$ \begin{aligned} {}_{15}P_{4} &= \frac{15!}{(15-4)!} \ &= \frac{15!}{11!} \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} {}_{15}P_{4} &= 15 \times 14 \times 13 \times 12 \ &= 32760 \end{aligned} $$ 32760 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Permutations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the permutation parameters

Apply the permutation formula

Calculate the final value

Answer: