{
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 254251200 permutations.\n"
     ]
    }
   ],
   "source": [
    "# Permutations\n",
    "import numpy as np\n",
    "from scipy.special import perm\n",
    "\n",
    "N = 50\n",
    "k = 5\n",
    "p = perm(N, k, exact=True)\n",
    "print(f\"There are {p} permutations.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "050b72b4-628a-4d72-99d2-80deef2ad277",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 2118760 combinations.\n"
     ]
    }
   ],
   "source": [
    "# Combinations\n",
    "import numpy as np\n",
    "from scipy.special import comb\n",
    "\n",
    "N = 50\n",
    "r = 5\n",
    "c = comb(N, r, exact=True)\n",
    "print(f\"There are {c} combinations.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6a148101-89c9-4da4-8524-7971c46ea096",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a 0.9997198781738114 probability.\n"
     ]
    }
   ],
   "source": [
    "# Birthday problem\n",
    "import numpy as np\n",
    "from scipy.special import perm\n",
    "\n",
    "N = 365 # number of days\n",
    "k = 75 # Number of people registered\n",
    "\n",
    "p = perm(N, k, exact=True)\n",
    "prob_Eprime = p / (N**k)\n",
    "prob_E = 1-prob_Eprime\n",
    "\n",
    "print(f\"There is a {prob_E} probability.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80e1981c-0da9-4827-ac66-bd216cb592f1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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