EX 08/02

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\[\begin{aligned} A(n) &= n(n-1)(n-2) \cdots (n-k+1)& \\ &=\frac{n(n-1)(n-2) \cdots (n-k+1) \times {\color{DarkRed}(n-k)(n-k-1)\times \cdots\times 1}}{{\color{DarkRed}(n-k)(n-k-1)\times \cdots\times 1}}& \\ &=\frac{n!}{(n-k)!}. \end{aligned}\]

\[\begin{aligned} B(n) &= (n+1)(n+2) \cdots 2n& \\ &=\frac{{\color{DarkRed}1\times 2\times \cdots n} \times (n+1)(n+2)\cdots 2n}{{\color{DarkRed}1\times 2\times \cdots n}}& \\ &=\frac{(2n)!}{n!}.& \end{aligned}\]

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code : 3531