{"abstract":"Ordered arrangements overcount each selected subset.","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. Unordered samples without replacement. Exact operational definition: math.comb(n,k)","evaluation_group":"model-fc70f2ee83b43969","failed_approach":"The multiset coefficient permits repeated selections.","family":"xn-unordered-samples-without-replacement","id":"FA-5596","implementations":{"attempt":{"sha256":"14e6cf4e7c19d65d7bc36ba87dbc2bdd231dacd8550b9e07af1a680835814fad","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-1,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)), 10)\ncheck('fixture 2: (3, 0)', solve(*(3, 0)), 1)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 1)\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":"f4912516abf93a03f8b748529bbe0cef4dbb3c1578d5853b2383eed5833fb377","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.perm(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)), 10)\ncheck('fixture 2: (3, 0)', solve(*(3, 0)), 1)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 1)\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"},"fixed":{"sha256":"02fcb7d6354aa7c9200a3979343476c271efa4fa23c22ba26f438dd11bb2f8cb","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)), 10)\ncheck('fixture 2: (3, 0)', solve(*(3, 0)), 1)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 1)\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-unordered-samples-without-replacement","generated_at":"2026-09-29T14:37:51.172721+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(n,k)","root_cause":"Ordered arrangements overcount each selected subset.","sha256":"fb7e7142ddd958ea66b5f08c37c586c54dab8eb554b3ee055aaa655a57784c6e","title":"Unordered samples without replacement · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.601,"exit_code":1,"observations":[{"actual":15,"check":"fixture 1: (5, 2)","expected":10,"passed":false},{"actual":1,"check":"fixture 2: (3, 0)","expected":1,"passed":true},{"actual":10,"check":"fixture 3: (3, 3)","expected":1,"passed":false},{"actual":4,"check":"fixture 4: (2, 3)","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 15, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 10, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 4: (2, 3)\", \"actual\": 4, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.377,"exit_code":1,"observations":[{"actual":20,"check":"fixture 1: (5, 2)","expected":10,"passed":false},{"actual":1,"check":"fixture 2: (3, 0)","expected":1,"passed":true},{"actual":6,"check":"fixture 3: (3, 3)","expected":1,"passed":false},{"actual":0,"check":"fixture 4: (2, 3)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 20, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 6, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 4: (2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.472,"exit_code":0,"observations":[{"actual":10,"check":"fixture 1: (5, 2)","expected":10,"passed":true},{"actual":1,"check":"fixture 2: (3, 0)","expected":1,"passed":true},{"actual":1,"check":"fixture 3: (3, 3)","expected":1,"passed":true},{"actual":0,"check":"fixture 4: (2, 3)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 10, \"expected\": 10, \"passed\": true}, {\"check\": \"fixture 2: (3, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (2, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}