{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2c866c75-3d07-4686-9cd3-b7fd0c4f4065",
   "metadata": {},
   "source": [
    "# The factorial of 4\n",
    "\n",
    "4! = 4 × 3 × 2 × 1 = 24"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4feb470d-e239-4d01-b00e-327cf37c07bd",
   "metadata": {},
   "source": [
    "n! = n * (n-1) * (n-2) * (n-3) * ... * 1"
   ]
  },
  {
   "attachments": {
    "3b8eaeae-4293-4765-b567-6b9959cfed5a.png": {
     "image/png": "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"
    },
    "a1c54eee-2720-49ce-8b80-9bbe33e9134a.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAArcAAAA8CAIAAADzFwUSAAAT3klEQVR4Ae2deWwV1RfHT0WkQEsJQrEQhNIigmJNZJEIka0WC23CUilKoIYdCVtZSiViZUsaNRFBsdWgGESMFFkKRH7sRShRhAYDZaksBUqxpUWW9r1p7y+/3PxuJrO9uXdmXue9nvcH3Llzl+/5nPvOO30zcx8QfCEBJIAEkAASQAJIQIsAaFViHRJAAkgACSABJIAECGYJuAiQABJAAkgACSABbQKYJWhzwVokgASQABJAAkgAswRcA0gACSABJIAEkIA2AcwStLlgLRJAAkgACSABJIBZAq4BJIAEkAASQAJIQJsAZgnaXLAWCSABJIAEkAASwCwB1wASQAJIAAkgASSgTQCzBG0uWIsEkAASQAJIAAlgloBrAAkgASSABJAAEtAmgFmCNhesRQJIAAkgASSABDBLwDWABJAAEkACSAAJaBPALEGbC9YiASSABJAAEkACmCXgGkACSAAJIAEkgAS0CWCWoM0Fa5EAEkACSAAJIAHMEnANIAEkgASQABJAAtoEMEvQ5oK1SAAJIAEkgASQgIuyhKKiIpf74/Tp0y5XaK8893vEjL23bt36888/NVtadGhA86moqDh48GBubu6ePXtu3brlBB/NMbFSgMC9e/f27NmzYcOGzZs3X7hwQWAEp7uYWU5OazA/vkFMMD+I21pWVFRs2rTp8uXLtgsTzxJOnTo1evTo4VqvUaNGLVy4cMeOHVVVVWYUezye+fPnf/HFF2YaN1Sburq69PT0rKysurq6htLgt3kDwiM+ady6dWvu3LmhoaErV65UN7bi0IDmU1VVlZGR0bx5c/j/KyQkJC0trby8XE7JCh/5OFi2QsDj8SxatCg8PPz/vvrf/ykpKffv37cyrI19TS4nG2e0MpRxTLAycoP3HTFiBABERkbW19fbK0Y8SyCESJK0du1atnyTk5P37NmzefPmrKysDh06AECrVq3WrVtnrPjGjRuDBg3atWuXcTOXnM3JyUlISHjw4IFL9DghI7A8okng9u3b8+fPZx+EmlkC7Sjg0IDmU15e3qNHDwAICQlp1aoVe/MCQKdOnSoqKhQ8BfgoRsBDYQK1tbXJycmtWrUaMWJEZmbmhAkTnn76aeqy/v37Cw9rY0fe5WTj1LxDmY8JvCO7pD17OxcXF9sryVKWQAg5d+4cCzTXr19n4h49evTKK6/QU7m5uaxeUbh582ZUVNRPP/2kqHfz4cKFC0eOHClJkptFCmsLRI8ojC0oKFizZs3Ro0cnTpxIV6BBlkAI4XJooPMZMWJEVFRUXl7evXv3CCF3795dvXp1kyZNKKhRo0YpYPLyUXfHGmECc+bMSUhIuH37NhuhrKyMxdWdO3ey+oYqCCynBpHKGxMaRKSVSaurq9kH8cGDB60Mpe5rNUv44YcfqLhevXopRt+1axc91aFDB8UpeujxeF577bXJkydrnnVtpSRJL7744qxZs1yrUFhYgHpEz969e/fSFWicJZh3aKDzOXLkSGRk5M2bNxXE2FsVAO7cuaM4a56PoiMeWiFw7dq1wYMHezwexSCnTp2iq3rJkiWKU34+FFtOfhapmM5kTFD0cv9hfX39U089RReG3m1YwlZYzRImT55MlS1evFgh4sqVK/QUAJSVlSnOEkLmzp3bvHlzdVRSt3Rbzfbt2wHA5TdSCEALXI9oGnv48GG6Ao2zBEKISYcGOp8JEyZ8//33mqwSEhIoq/z8fHUDk3zUHbFGmMCWLVtKSkrU3evr61u0aAEAy5cvV5/1Z43wcvKnSMVc5mOCoqP7D7t27UrfwurrhhbFW80SOnXqRJUdOnRIIeXSpUv0FACUlpYqzh44cAAApk+frqgPlMMuXbq0bt367t27gSLYp85A94jaQK6I4NOhQcDn9ddf17v3dsOGDfTdmpOToyZJCPHJR7MXVtpOoKKignrqt99+s31wrgGtLCeuiWxszBUTbJzXD0MNGzYMAFq2bGn7XJayhL/++ouu1/DwcPU3Y/v376dn27Vrp9adnJwMAPv371efCoiaxYsXA8CiRYsCQq0ZkYHuEbWNXBHBp0ODj4+cGP22AAD0Pnt88pGPxsrbt29PS0v75JNPWI1mQZKkzMzMtLS0goICzQZurvSzjTt27ACASZMmcTHxs0ify0lTvB9EcsUETZGurZw6dSoA9OjRw3aFlrKETz/9lOYBmjc9TZs2jZ5VX8K/evXqE0880axZM3VuQQjxeDxnzpzZuHHjnDlzBg4cOG/ePGr2nTt3pkyZ0q5du86dO1u84dH6FLt37waAdu3aaZpgu59MDihsV4N7xKSBXM24IoKxQ4OSjxwmfVipadOm//77r7yelY35sGaKgtfrHTNmDAAsXbpUcYodSpKUmpoKAOydzk4FRMGfNt67dy86OjotLa22tpYLjj9FEkJ8LidN8X4QyRUTNEU6XSkcw9esWQMACQkJtiu0lCW88cYbNA9Qf0t56NChpk2bAsCzzz6r/lo+IyMDAOLi4jTtOXz48KxZsyIjI+ngv/zyCyHk8uXL3bt3Hzp0KL0m1759e82+JiutT1FSUkLl7d692+SkfmgmbFeDe8QJOFwRwdihQclHznzSpEkAMHXqVHmlvGzMR95SUTYO/ZIkjR8/PnBTBGqsf2wsLi7u169f27ZtxZ4b949ICsTnclIsEnbotEiumMBU+bMgHMO3bt1q/BYWtkI8S3j8+HFoaCj9pGTPQEqSdPLkySVLltD7LZ9//nnNZzdfeuklAEhNTTXQ/cEHHwBAaGjow4cPz58/P2DAALqr1JQpU+y6+mJlirq6Ovo4fkZGhoEV7NSNGzeWWXh9+OGHbCifBQG7XOIRn6ZxNeCKCMYODUo+DOaDBw/CwsKaNm36999/s0pFwZiPorHiUC/0B0eKQI111MaLFy+mp6ez/T8AYOLEiY8fP1Zw9nnoqEg2u5nlxBqrC46K5IoJCm0uj+G///47AKxYsUIh2/qheJawb98+miIAQERERGxsbKdOnVq2bEk3bImLi1u7dq3mOn78+PGTTz4JALNnzzYwICkpCQCSkpLu378/bNgw9ijEqFGjAGDAgAEGfU2esjhFXFwcAAwaNMjMdCdPnmS4BAqhoaFmZqFteO1yj0fM22imJW9E0HNosPJhDD/77DMA8Hn3gB4fNo5BQR36gylFoIY7ZGNlZeXSpUvnzZs3fPhwGjlpAFmwYIEBcL1TDomUT2dyOcm7KMrOieSNCXJhbo7hhJB//vkHAL777ju5ZlvK4lnCvHnz6GKdOXNmYWHhzp07t23blp+fX1hYqL7EINd69epV2tHgr3BJkiIiIgAgNzc3NTX16NGjbAS6q+P777/PasQK1qcYMmQIAHTt2tWMgOrq6v9YeJnfKEPALpd4xAxGrja8EUHPocHKh8IsKyuLiIhISkryubGrHh+TTpGHfkmS3n77bYsXGh4+fFhUVKT31IZclRMt5eOzsu02spFpoby8fNy4cTR+NmnS5Ny5c4oGZg4dFWl+ORlLdUgkb0yQi3RzDKc6W7RooX7YUG6CWFk8S6D7vALAvn37uOY+e/YsXeUfffSRXkeatYWEhGRnZ69evZo1u3jxIu175MgRVilWsD4F3Tc7IiJCTIBDvQTs8qdHjh07pvXTH6bqqquruaDxRgQ9hwYrHwozJSWld+/eZjYd1+Nj3iks9Pfs2dNiiuD1emNiYgDgzTffNBbgREuDGW20UW+WCRMm0DC4atUqvTbG9c6JNL+cjBUSQpwQyRsTfIp0ooFADKcyunbteuXKFdslCWYJ169fp8u0WbNmjx494pJVXFzsM0tYsWIFAHTs2DExMVH+Jw59qjssLMz6kwXWp6CPxoWEhHCZ73RjAbv86ZG9e/fGir4qKyu56PFGBD2HBisfQsiqVat69uxp/OUfY67HhzUwU6ipqenYsSMA9O7d20x7vTbHjx+nYQQAjLeRcaKlnipab5eNerOUl5fTe8OtbFzrhEiu5aRnnbzedpG8MUEuxm9lgRhOtfXv35/34RczRglmCbm5ufQtOmzYMDPTyNvcvXuX9s3MzJTXy8sDBw6k9zcoftv3rbfeAoCRI0fKG4uVrU8RHx8PAOHh4WICHOolYJdLPGI7EN6IoOfQYOWTl5fXrVs3vZ+NVrtDj4+6pV4Nu9AQGxsLAFb2GPZ4PPTrzKSkJL3paL0TLQ1mtNFGg1kGDRpE72E0aGNwygmRvMvJQB495YRI3pjgU6QTDQRiOJVh8IySFZ2CWQJ9BhoAsrOzeaeXJIk+ATFz5kzNvtXV1fQmneTkZHmD+vr6tm3bAoDP35mU99Is2zLFq6++CgAxMTGaUygqa2trS629FANqHorZ5QaPaJpjsZI3Iug5NCj5HDhwoFu3blevXjUPWY+PyRHktyt6PB4aQ9Q7u5scjRBSV1dn8FCGfBwnWsrHZ2XbbWQjKwrvvPMOAIjdnuWESIHlpLBIceiESEIIb0yQq3JzDKc6FX9Uy8VbKYtkCZIktW7dmn4fcObMGYHpabjR+x6C7dv166+/ygc/ffo0nfTSpUvyeoGyLVN0794dAMaOHWtGAL3URPUL/GvyGQdhuxrcI2YY8rbhjQgGDg0yPidPnoyJidF8SpkQUlBQIL/Mx7Ab8GFt9ArqrZO8Xu/o0aODaQNTf9o4YMAAADh27JgecL16J0SKLSc9hYQQJ0TS6Xhjglyky2O4XKq9ZZEsgV3na9++vWY08SkxPT2d3nag2XLGjBkAEBkZqfh15uzsbACIjo6mvb766ivN7lVVVZr18kqLU9ANIumlQZNfbFy8eHGshdf48ePl+vXKwnY56hE9tU7Xc0UEj8dj4NBg4lNUVBQbG1tUVKTJ//Lly+PGjVOfMuajbi+vkSSJ3pmv2F2RJQoLFy6Utw/Esj9trKysDAsL69OnD2/4dUKk2HIycLETItl0XDGB9aIFl8dw+u2aQjM9rK2tZXsaaTYwrhTJEpYsWUL/Gh4zZozx6HpnCwsL6Qiad61HR0cDwIwZMxTdExMTAeDdd98lhKxfv1798VxaWkr7+vxMFZ6CSaK/YREWFqZpAmvm54KwXQ55xM/mK6bbtm0bXWZZWVmKU+pDY4cGDZ9Lly4988wzkydP3qB6ffnll8uXL4+MjNy2bRsvH3V7VuP1euntRIoUgTbweDz0GwWxp//ZLA1bcMLGioqKnJycwsJCtWkZGRmtW7fmfQzSCZHCy0ltFK1xQqR8Lq6YIO/ot7JwDM/Ozg4PD4+Pj6+pqZGrLSsr69KlCwD4/FiU95KXubOEysrKqKgoGnx93jckn0lR7tWrFwAorikQQtj95Hv37lV0ee655wBg9OjRH3/8sfq3IQghGzdupMIA4MSJE4ru7NDKFGwQulH5e++9x2oavGDRLic80rBMpk+fTtdDSkqKTyU+HRoEfG7cuNG5c2f2HtEstG/fXvMBIp98NAl7vd6UlBTjhx49Hg/dKm3+/Pmag7i80iEbly1bRh2UmJjIEoKampply5a9/PLLvFegnRBpZTlp+tQJkYqJuGKCoq8fDoVjuMfjoVsaAoDio/Obb75h73Tex8SoyXxZwowZM+imRmzWIUOGrF27VgDfzz//DADTpk1T9P38888BICwsTJEQEULGjh1LH3xIT0/X3Erl7NmzbBPTTZs2KUZmh1amYIMMHjw4JCTk/PnzrKbBCxbtcsIjDcLk2rVrmZmZCQkJbJXSp+ozMzPl23MptPl0aKDz8Xq99MYCORZ1We9nmXzyUfCkh1u3bk1NTV25cqXmWVbp8XgWLFiQmppqfvcw1rfBCw7ZeOLEiTZt2lAHhYSE9OzZs2/fvnFxcT/++CPvhQZCiO0iLS4nTa/ZLpLNIhYTWHe/FazE8L59+wJAmzZtSktL5YIvXLhAf/yoT58+8nrzZb4swfy4ZloOHTo0IiLCfHbz8OHD48ePl5WVGQxeVVV1+vTp6Oho9bcUBr3YKTNTEELoNjvLly9nHV1eMGmXEx5xORkqz6RDkU9AeDNoRN6/fz8/P3/9+vU5OTl5eXklJSVBYxoawkvAZwyXJOmPP/7Q/FWE69ev5+fn8+5sxBQ2ZJZQXl4eExNj5ZlpZoaiEBcXZz75UPT1eVhXVxcfHz98+HDN7zN8dndzA+c84marzTsU+bjZj6gNCSABJwg0ZJZA70KIiooyuIdAwOavv/7a5zecAsOyLllZWV26dDHe7o01DrhCcXGx7R5xOQQuhyIfl3sT5SEBJGAvgQbOEujD2S+88MK1a9dsMezbb7919ELA9u3b+/Xrx7UXjS12+XOQgoICGz3iT+UCcwk4FPkIcMYuSAAJBCiBhs8SCCElJSWJiYkGd5aZhyuwzYj5wdetWzd79mwnNso2r8E/LW30iH8Ei80i7FDkIwYceyEBJBBwBFyRJRBCampqtmzZ4mZ8Xq83Ly/PzQrt1eZ+j1i016JDkY9F/tgdCSCBgCDgliwhIGChSCSABJAAEkACjYoAZgmNyt1oLBJAAkgACSABDgKYJXDAwqZIAAkgASSABBoVAcwSGpW70VgkgASQABJAAhwEMEvggIVNkQASQAJIAAk0KgKYJTQqd6OxSAAJIAEkgAQ4CGCWwAELmyIBJIAEkAASaFQEMEtoVO5GY5EAEkACSAAJcBDALIEDFjZFAkgACSABJNCoCGCW0KjcjcYiASSABJAAEuAggFkCByxsigSQABJAAkigURHALKFRuRuNRQJIAAkgASTAQQCzBA5Y2BQJIAEkgASQQKMigFlCo3I3GosEkAASQAJIgIPAfwG69muADNSZugAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "cdb13968-5c24-4578-b49b-88524fdccc0b",
   "metadata": {},
   "source": [
    "# Permutations\n",
    "\n",
    "Given a set of n elements, we can construct all possible permutations by selecting the elements one at a time. The first element can be chosen in n different ways. The second element in (n − 1) ways, the third in (n − 2) ways, etc. Thus, the number of all permutations that are possible with n elements is:\n",
    "\n",
    "![image.png](attachment:a1c54eee-2720-49ce-8b80-9bbe33e9134a.png)\n",
    "\n",
    "If we start with n elements and construct the permutations with k positions, the first element can be chosen in n different ways. There are n − 1 elements left for the next k − 1 positions. The second position has n − 1 elements, the third n − 2, and so on;\n",
    "\n",
    "![image.png](attachment:3b8eaeae-4293-4765-b567-6b9959cfed5a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "453299bb-e619-4f81-88e1-081a7776a0b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]\n",
      "6.0\n"
     ]
    }
   ],
   "source": [
    "from itertools import permutations\n",
    "import math\n",
    "\n",
    "arr = [1,2,3]\n",
    "\n",
    "a = list(permutations(arr, 2))\n",
    "print(a)\n",
    "\n",
    "b = math.factorial(len(arr))/math.factorial(len(arr)-2)\n",
    "print(b)\n",
    "\n",
    "assert len(a) == int(b)"
   ]
  },
  {
   "attachments": {
    "d3760c07-918f-43a4-a6a6-347dd2cebb2e.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "992089cf-d22e-4f7e-8844-607b9c61ec84",
   "metadata": {},
   "source": [
    "# Combinations\n",
    "\n",
    "![image.png](attachment:d3760c07-918f-43a4-a6a6-347dd2cebb2e.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "deddc637-af6f-42ac-98fd-a607348dd455",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
