Question 5351: Full Product Choices and Prefix Counts

Original question and givens

Ordered stage sizes=[]; every cross-stage combination is allowed. Give (full product count, each prefix product). Zero stages have one empty selection sequence.

• G001 — Ordered stage sizes=[]; every cross-stage combination is allowed. Give (full product count, each prefix product). Zero stages have one empty selection sequence.

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-counting-principle

Step-by-step derivation

declared finite tagged choices or full-product protocol

combinatorial counts,not probabilities or independence

ordered sizes=[]

initial accumulator=1

Reverse checks

• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(1, [])

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.