curl --request POST \
  --url https://api.iotools.cloud/v1/tool/derangement-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '{
  "n": "5"
}'

{
  "tool": "derangement-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "results": [
      {
        "metric": "Derangements !n",
        "value": "44"
      },
      {
        "metric": "Total permutations n!",
        "value": "120"
      },
      {
        "metric": "Probability (!n / n!)",
        "value": "0.366666"
      }
    ],
    "steps": "!5 = (n − 1) × (!(n − 1) + !(n − 2))\nBuilt up from !0 = 1 and !1 = 0 to !5 = 44\nn! = 120\nDerangement probability = !n / n! = 44 / 120 ≈ 0.366666"
  },
  "credits_used": 5,
  "credits_remaining": null
}