{"abstract":"Unordered selection drops permutation multiplicity.","category":"Combinatorics","checks":4,"contract":"Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Ordered samples without replacement. Exact operational definition: math.perm(n,k)","contract_signature":"n, k","evaluation_group":"model-9c41503f751a9e84","failed_approach":"Allowing replacement repeats objects that must be distinct.","family":"xn-ordered-samples-without-replacement","id":"FA-5591","implementations":{"attempt":{"sha256":"34c97a84b50825f96ec731018764babb776f6a38bbf3dfc9ca396b99a1188cad","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n, k):\n    return n**k\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 2)', solve(*(5, 2)), 20)\ncheck('fixture 2: (3, 0)', solve(*(3, 0)), 1)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 6)\ncheck('fixture 4: (2, 3)', solve(*(2, 3)), 0)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"82f5c5427696e83e91a5d69e6c4c09766a7dc975509f10a1e21f5e4c895bae73","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n, k):\n    return math.comb(n,k)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 2)', solve(*(5, 2)), 20)\ncheck('fixture 2: (3, 0)', solve(*(3, 0)), 1)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 6)\ncheck('fixture 4: (2, 3)', solve(*(2, 3)), 0)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-ordered-samples-without-replacement","generated_at":"2026-09-29T14:37:51.070176+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.","root_cause":"Unordered selection drops permutation multiplicity.","sha256":"ae9c10499854a2405d82b72124a64939adfbdaadb56aa29e90440b9068430b7c","title":"Ordered samples without replacement · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.503,"exit_code":1,"observations":[{"actual":25,"check":"fixture 1: (5, 2)","expected":20,"passed":false},{"actual":1,"check":"fixture 2: (3, 0)","expected":1,"passed":true},{"actual":27,"check":"fixture 3: (3, 3)","expected":6,"passed":false},{"actual":8,"check":"fixture 4: (2, 3)","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 25, \"expected\": 20, \"passed\": false}, {\"check\": \"fixture 2: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 27, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (2, 3)\", \"actual\": 8, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.456,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: (5, 2)","expected":20,"passed":false},{"actual":1,"check":"fixture 2: (3, 0)","expected":1,"passed":true},{"actual":1,"check":"fixture 3: (3, 3)","expected":6,"passed":false},{"actual":0,"check":"fixture 4: (2, 3)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 10, \"expected\": 20, \"passed\": false}, {\"check\": \"fixture 2: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 1, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}