Integer permutations count

integer-permutations-count · version 1.0.0 · Numbers & math · free, no key needed

Compute the exact number of k-permutations of n distinct items, P(n, k) = n! / (n-k)!.

Use when you need to: integer permutations count · n permute k · arrangements count.

Supported

• integer permutations count
• n permute k
• arrangements count

Not supported

• binomial coefficient
• permutations with repetition
• negative n or k

Behavior

• 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.

Input

• n (integer, required): min 0; max 100000
• k (integer, required): min 0; max 100000

Output

• value (string, required)

Limits

• max n: 100000
• max digits: 1000

Example

Request input:

{
  "n": 5,
  "k": 2
}

Response:

{
  "result": {
    "value": "20"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "integer-permutations-count",
  "version": "1.0.0",
  "input": {
    "n": 5,
    "k": 2
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-permutations-count/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"n":5,"k":2}'

The machine-readable contract is at /v1/tools/integer-permutations-count/versions/1.0.0.

CLI

node cli.mjs run integer-permutations-count 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Integer binomial coefficient: Compute the exact binomial coefficient C(n, k), the number of ways to choose k items from n.
• Integer derangements count: Compute !n, the number of derangements (permutations with no fixed point) of n items, exactly.
• Array integer GCD: Compute the non-negative greatest common divisor of an array of canonical integer strings.
• Array integer LCM: Compute the non-negative least common multiple of an array of canonical integer strings.
• Integer factorial: Compute n! (n factorial) exactly for a bounded non-negative integer n.
• Integer totient: Compute Euler's totient function: the count of integers in [1, value] coprime to value.