{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260930-r06-selection-model-choice-0011", "pilot_number": "R0069-35061", "number": 35061, "family_id": "qf-selection-model-choice", "title": { "zh-Hant": "第 35061 題：選取模型判定", "en": "Question 35061: Choosing a Selection Model" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260930-r06-selection-model-choice-0011", "batch_id": "batch-20260930-r06-permutation-combination-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-permutation-combination" ], "title_zh": "選取模型判定", "stem_zh": "從 5 個彼此相異物件無放回且不重複選取 2 個，空選取計一種。本題區分選取順序，應使用排列模型還是組合模型？", "answer": { "kind": "short_text", "value": "排列", "explanation_zh": "相異性、無放回及不重複均已明示；順序有意義，所以選擇排列。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "順序條件", "無放回" ] }, "variant": { "family_id": "qf-selection-model-choice", "seed": 202609306211, "parameters": { "operation": "model_choice", "n": 5, "k": 2, "ordered": true, "replacement": false, "distinct": true, "semantic_template": "qf-selection-model-choice/{\"distinct\":true,\"k\":2,\"n\":5,\"operation\":\"model_choice\",\"ordered\":true,\"replacement\":false}" } }, "verification": { "status": "candidate", "checks": [ "json_schema", "producer_local_answer_invariants", "explanation_witness_accuracy" ], "warning_zh": "本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。" }, "provenance": { "generator_role": "question_producer", "generator_model": "Codex GPT-6 question producer", "generated_at": "2026-09-30", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260930-r06-selection-model-choice-0011", "batch_id": "batch-20260930-r06-permutation-combination-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "fd85ca20b53a6881975255f8cfee3629556dafbf681991dc0322e7c00d9e172d", "family_id": "qf-selection-model-choice", "seed": 202609306211, "semantic_template": "qf-selection-model-choice/{\"distinct\":true,\"k\":2,\"n\":5,\"operation\":\"model_choice\",\"ordered\":true,\"replacement\":false}" }, "fields": { "title": "Choosing a Selection Model", "stem": "Select k=2 objects with order distinguished, without replacement or repetition, from n=5 distinct objects. Should the model be a permutation or a combination?", "answer": { "kind": "short_text", "value": "permutation", "explanation": "The objects are distinct and selection is without replacement. Because order is significant, use the permutation model." }, "skills": [ "ordering condition", "without replacement" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "從 5 個彼此相異物件無放回且不重複選取 2 個，空選取計一種。本題區分選取順序，應使用排列模型還是組合模型？", "en": "Select k=2 objects with order distinguished, without replacement or repetition, from n=5 distinct objects. Should the model be a permutation or a combination?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-selection-model-choice, [distinct, k, n, operation, ordered, replacement]]", "after": "derived = [model_choice, no-invented-domain]", "relation": "implies", "rule_id": "R69_SOURCE_specific_keys_operation_domain_AND_binary_contract", "conditions": [], "explanation": { "zh-Hant": "各bank的keys/operation/domain獨立：LDL/PULSE/function legacy為表內underscore，TREE是完整tree_*與明定domain，BASE signed較寬不偷加op/domain。所有算術保持binary primitive契約。", "en": "Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。", "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [5, 2, 是, 否, 是]", "after": "derived = [ordered positions, 排列]", "relation": "implies", "rule_id": "Selection_EXACT_Boolean_distinct_no_replacement_ordering_MODEL", "conditions": [], "explanation": { "zh-Hant": "明示不同物件、無放回且不重複；ordered真就區分次序用排列，假就忽略次序用組合。即使k=0兩種個數都1，模型分類仍依原ordered條件；不是機率。", "en": "Given DISTINCT objects WITHOUT replacement/repetition,ordered=True distinguishes positions and uses permutations;False ignores order and uses combinations.Even when k=0 both counts are1,the MODEL still follows the ORIGINAL ordering premise.This is not probability." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。", "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged." } }, "arithmetic": null } ], "math_model": { "result": "排列" }, "conclusion": { "canonical_value": "排列", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20260930-r06-permutation-combination-foundations", "batch_path": "public/data/questions/batches/batch-20260930-r06-permutation-combination-foundations/questions.jsonl", "batch_sha256": "e40d1692407a43376f6370aae8b40042e482d2017d4ad08bd18bdf6694032044", "original_line": 61, "original_line_sha256": "de3f6d903e532843e2d268102548677c1db51a60b7b284470e1619ee16e3291c", "question_compact_sha256": "fd85ca20b53a6881975255f8cfee3629556dafbf681991dc0322e7c00d9e172d", "english_row_compact_sha256": "cf43dd2403161c77a157a364816c5dd01c01d243a4b987233ad1b9420e209668", "english_manifest_path": "public/data/i18n/editions/batch-20260930-r06-permutation-combination-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260930-r06-permutation-combination-foundations.en.jsonl" }, "mko_bindings": { "mko-permutation-combination": { "sha256": "bd1ee61b3eaee90e08b3bb7a753128635ac36421438a78c41bba6dc768077c96", "english_sha256": "d86418363f341c4360d50617abf179e87c404fcc7d85b191d8da6e74d8bb6200", "original_path": "public/data/mko/permutation-combination.json", "english_path": "public/data/i18n/editions/mko-permutation-combination.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "63155b87d4994521b4a60f8f179750f57cbbd094e66cc42652608d1bbab47a9f", "original_candidate_sha256": "75a1411db4ffbeb8e3ab08bd9bd29fff65dbc445f64b3bfb8a43a43eb1a002c5", "original_candidate_line_sha256": "75a1411db4ffbeb8e3ab08bd9bd29fff65dbc445f64b3bfb8a43a43eb1a002c5" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-012-p70", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b", "question_first_witness_sha256": "11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 2, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "616021884318378481b51dd64d06c280ea2cf34e16ee0c6b0ca7c55201b67b53", "arithmetic_steps": 0 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }