select the correct answer.

how many ways can the letters of the word organism be arranged so the third letter is g?

7
8
5040

Question

select the correct answer.

how many ways can the letters of the word organism be arranged so the third letter is g?

7
8
5040

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Permutations with Constraints", "Factorial Calculations" ], "current_concepts": [ "Permutations with Constraints", "Factorial Calculations" ] } ## Identify the letters and constraints $$ \begin{aligned} &\text{Word: } \text{ORGANISM} \ &\text{Total letters } (n) = 8 \quad (\text{O, R, G, A, N, I, S, M - all unique}) \ &\text{Constraint: Third letter must be } G \quad (\text{1 choice for the 3rd position}) \end{aligned} $$ ## Calculate the remaining arrangements $$ \begin{aligned} &\text{Remaining positions to fill} = 8 - 1 = 7 \ &\text{Remaining unique letters} = 7 \ &\text{Number of ways} = 7! \end{aligned} $$ ## Compute the final value $$ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 $$

7

8

5040

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Permutations with Constraints" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the letters and constraints

Calculate the remaining arrangements

Compute the final value

Answer: