2018-04-07-3-3.ipynb

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    "### 順列や組合せを式 nPr nCr を用いて計算できる\n",
    "- No: 3\n",
    "- Sub No: 3\n",
    "- 難易度: ★\n",
    "- カテゴリ名: 統計数理基礎\n",
    "- 必須スキル: ◯\n",
    "\n",
    "\n",
    "\n",
    "### 順列・組合わせ\n",
    "- 順列\n",
    "  - 異なるn個からr個を取り1列に並べる場合の数\n",
    "  - $$_nP_r$$ (Permutations)\n",
    "- 組合わせ\n",
    "  - 異なるn個からr個を取る選び方の数\n",
    "  - $$_nC_r$$ (Combinations)\n",
    "\n",
    "\n",
    "\n",
    "### Juliaでの順列・組合わせ例\n",
    "```julia\n",
    "using Combinatorics\n",
    "# 扱う配列 ['A','B','C','D']\n",
    "```\n",
    "\n",
    "\n",
    "## 順列\n",
    "```julia\n",
    "collect(permutations(['A','B','C','D'], 2))\n",
    "# 異なる4個の中から異なる2個を取り出して1列に並べる\n",
    "12-element\n",
    "['A', 'B'] ['A', 'C'] ['A', 'D']\n",
    "['B', 'A'] ['B', 'C'] ['B', 'D']\n",
    "['C', 'A'] ['C', 'B'] ['C', 'D']\n",
    "['D', 'A'] ['D', 'B'] ['D', 'C']\n",
    "```\n",
    "\n",
    "\n",
    "$$_nP_r=n×(n-1)×(n-2)...(n-r+1)$$\n",
    "\n",
    "$$_nP_r=\\frac{n!}{(n-r)!}$$\n",
    "\n",
    "$$_4P_2=4×3=12$$\n",
    "\n",
    "\n",
    "## 組合わせ\n",
    "```julia\n",
    "collect(combinations(array, 2))\n",
    "# 異なる4個の中から異なる2個を取り出す選び方\n",
    "6-element\n",
    "['A', 'B'] ['A', 'C']\n",
    "['A', 'D'] ['B', 'C']\n",
    "['B', 'D'] ['C', 'D']\n",
    "```\n",
    "\n",
    "\n",
    "$$_nC_r=\\frac{_nP_r}{r!}=\\frac{n!}{r!(n-r)!}$$\n",
    "\n",
    "$$_4C_2=\\frac{_4P_2}{2!}=\\frac{4×3}{2×1}=6 $$"
   ]
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