Question Number 135472 by mr W last updated on 13/Mar/21 | ||
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$${for}\:{x}+{y}+{z}=\mathrm{10}\:{with}\:{x},{y},{z}\in\mathbb{N} \\ $$$${find}\:\Sigma\frac{\mathrm{10}!}{{x}!{y}!{z}!} \\ $$ | ||
Answered by Ñï= last updated on 13/Mar/21 | ||
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$$\Sigma\begin{pmatrix}{\:\:\:\mathrm{10}}\\{{x},{y},{z}}\end{pmatrix}=\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{10}} =\mathrm{3}^{\mathrm{10}} \\ $$ | ||