there are four doors to an office. in how many ways can an employee enter the office through one door and leave the office through a different door?

a 4
b 5
c 12
d 16
e 20

Question

there are four doors to an office. in how many ways can an employee enter the office through one door and leave the office through a different door?

a 4
b 5
c 12
d 16
e 20

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": [ "Fundamental Counting Principle", "Permutations" ], "current_concepts": [ "Fundamental Counting Principle", "Permutations", "Combinatorics" ] } ## Identify choices for entering the office $$ N_{\text{enter}} = 4 $$ ## Identify choices for leaving the office $$ N_{\text{leave}} = 4 - 1 = 3 $$ ## Calculate total number of ways $$ N_{\text{total}} = N_{\text{enter}} \times N_{\text{leave}} = 4 \times 3 = 12 $$

(A) 4

(B) 5

(C) 12

(D) 16

(E) 20

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Fundamental Counting Principle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify choices for entering the office

Identify choices for leaving the office

Calculate total number of ways

Answer: