Select k=0 objects in order, without replacement or repetition, from n=0 distinct objects. The empty selection counts once. Find P(0,0).
G001 — Select k=0 objects in order, without replacement or repetition, from n=0 distinct objects. The empty selection counts once. Find P(0,0).
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.
source roles = [qf-permutation-exact-count, [k, n, operation]]
After
derived = [permutation, no-invented-domain]
Conditions: none
Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.
Choose ordered positions from n DISTINCT objects WITHOUT replacement.Position i has n−i+1 choices.For k=0,the empty selection counts ONCE and the product starts at1.THIS bank permits n≤200,not another bank’s32/64 cap.
The multiplication principle combines ALL k position counts,giving P(n,k)=n!/(n−k)!.This is a count,not probability.The empty product is1 and derived BigInts are not truncated to SAFE.
S003 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S002 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
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.