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The $k$-th moment of the $(n-1)$-dimensional volume of a random $(n-1)$-simplex is monotone under set inclusion, if $K \\subseteq L$ implies that the $k$-th moment of $V_{K[n]}$ is not larger than that of $V_{L[n]}$. Extending work of Rademacher [On the monotonicity of the expected volume of a random simplex. 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