数学 - JavaScript - 「場合の数」 を数える - 順列・組合せ – 順列 - 重複組合せ

数学読本〈4〉

学習環境

• Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
• Windows 10 Pro (OS)
• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

数学読本〈4〉数列の極限，順列/順列・組合せ/確率/関数の極限と微分法(松坂 和夫(著)、岩波書店)の第15章(「場合の数」 を数える - 順列・組合せ)、15.2(組合せ)、重複組合せ、問24、25、26、27、28.を取り組んでみる。

24. 
    $\left(\begin{array}{c}3+10-1\\ 10\end{array}\right)=\left(\begin{array}{c}12\\ 10\end{array}\right)=\left(\begin{array}{c}12\\ 2\end{array}\right)=66$
25. 
    $\left(\begin{array}{c}6+6-1\\ 6\end{array}\right)=\left(\begin{array}{c}11\\ 6\end{array}\right)=\left(\begin{array}{c}11\\ 5\end{array}\right)=\frac{11·10·9·8·7}{5·4·3·2·1}=11·3·2·7=462$
26. 
    $\left(\begin{array}{c}4+3-1\\ 4\end{array}\right)·\left(\begin{array}{c}3+3-1\\ 3\end{array}\right)=15·10=150$
27. 
    $\left(\begin{array}{c}\left(n+1\right)+r-1\\ r\end{array}\right)=\left(\begin{array}{c}n+r\\ r\end{array}\right)$
28. 
    $\begin{array}{l}\left(\begin{array}{c}2+5\\ 5\end{array}\right)=\left(\begin{array}{c}7\\ 5\end{array}\right)=21\\ \left(\begin{array}{c}3+5\\ 5\end{array}\right)=\left(\begin{array}{c}8\\ 5\end{array}\right)=56\end{array}$

コード(Emacs)

HTML5

<button id="run0">run</button>
<button id="clear0">clear</button>
<pre id="output0"></pre>
<script src="sample24.js"></script>

JavaScript

let btn0 = document.querySelector('#run0'),
    btn1 = document.querySelector('#clear0'),
    pre0 = document.querySelector('#output0');

let permutation = (n, r) => {
    let iter = (i, result) => {
        if (i > n) {
            return result;
        }
        return iter(i + 1, i * result);
    };
    return iter(n - (r - 1) , 1);
};
let factorial = (n) => {
    return n <= 1 ? 1 : n * factorial(n - 1);
};

let combination = (n, r) => {
    return factorial(n) / (factorial(r) * factorial(n - r));
};

let combinationsWithRepetition = (n, r) => {
    return combination(n + r - 1, r);
};

let output = () => {
    pre0.textContent =
        '24.\n' +
        `${combinationsWithRepetition(3, 10)}\n` +
        '25.\n' +
        `${combinationsWithRepetition(6, 6)}\n` +
        '26.\n' +
        `${combinationsWithRepetition(4, 4) * combinationsWithRepetition(3, 3)}\n` +
        '28.\n' +
        `${combination(7, 5)}\n` +
        `${combination(8, 5)}\n`;
};

btn0.onclick = output;
btn1.onclick = () => {
    pre0.textContent = '';
};

output();