{"id":"integer-permutations-count","version":"1.0.0","description":"Compute the exact number of k-permutations of n distinct items, P(n, k) = n! / (n-k)!.","supported_operations":["integer permutations count","n permute k","arrangements count"],"unsupported_operations":["binomial coefficient","permutations with repetition","negative n or k"],"semantics":["n and k are JSON integers with 0 <= k <= n <= 100000.","The result is P(n, k) = n * (n-1) * ... * (n-k+1), computed exactly with an incremental BigInt product (never materializing n! itself), never floating point.","P(n, 0) is 1 for every valid n; P(n, n) equals n!.","Requests whose exact result would exceed 1000 digits are rejected rather than truncated."],"limits":{"max_n":100000,"max_digits":1000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["n","k"],"properties":{"n":{"type":"integer","minimum":0,"maximum":100000},"k":{"type":"integer","minimum":0,"maximum":100000}}},"output_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string"}}},"examples":[{"input":{"n":5,"k":2},"output":{"value":"20"}}],"execute_url":"/v1/tools/integer-permutations-count/versions/1.0.0/execute"}