# Question 35066: Choosing a Selection Model

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0069-35066 · q-20260930-r06-selection-model-choice-0016



## Original question and givens

Select k=2 objects with order ignored, without replacement or repetition, from n=7 distinct objects. Should the model be a permutation or a combination?


- G001 — Select k=2 objects with order ignored, without replacement or repetition, from n=7 distinct objects. Should the model be a permutation or a combination?





## Definition and scope

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.


- [mko-permutation-combination](https://ocme.evemisslab.com/en/mko/mko-permutation-combination/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-selection-model-choice, [distinct, k, n, operation, ordered, replacement]]

After

derived = [model_choice, no-invented-domain]

Conditions: none

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.

Step identifiers and dependenciesRule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001





S002 · impliesBefore

source roles = [7, 2, No, No, Yes]

After

derived = [unordered subset, combination]

Conditions: none

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.

Step identifiers and dependenciesRule: Selection_EXACT_Boolean_distinct_no_replacement_ordering_MODEL · Uses: G001, S001









## Reverse checks


- S002 · premise_and_result_audit — 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.
- S001 · premise_and_result_audit — 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.





## Result

combination

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: a49a18e90c3bb7ec720079809d3d98c00dae99b4cd24f87bd4455748220fdebd
- candidate record SHA-256: 334759f03cdc268c90582114eb89f6fc48dc1efff558b6c558a9b7cfba0cf062
- semantic review receipt SHA-256: ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b
- question-first witness SHA-256: 11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260930-r06-selection-model-choice-0016.json)