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Question Number 209059 by hardmath last updated on 01/Jul/24

$$\mathrm{Compare}:$$$$8!\mathrm{and}8!!$$

Commented by Frix last updated on 01/Jul/24

$$n!!\ne (n!)!$$$$n!!=\{\begin{array}{l}{2}^{k}k!,n=2k\\ \frac{\left(2k\right)!}{2^{k}k!},n=2k-1\end{array}$$$$\Rightarrow 8!!=\left(2\times 4\right)!!=2^4\times 4!=16\times 24=384$$$$8!=40320$$$$8!=105\times 8!!$$

Commented by A5T last updated on 01/Jul/24

$$Itwasprobablyajoke.$$

Commented by mokys last updated on 01/Jul/24

$$n!=n(n-1)(n-2)(n-3)...$$$$n!!=n(n-2)(n-4)(n-6)...$$$$$$$$8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$$$$8!!=8\times 6\times 4\times 2$$

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