for-x-y-z-10-with-x-y-z-N-find-10-x-y-z-

Tinku Tara June 3, 2023 Algebra 0 Comments

Question Number 135472 by mr W last updated on 13/Mar/21

for x+y+z=10 with x,y,z∈N find Σ((10!)/(x!y!z!))

$${for}\:{x}+{y}+{z}=\mathrm{10}\:{with}\:{x},{y},{z}\in\mathbb{N} \\ $$$${find}\:\Sigma\frac{\mathrm{10}!}{{x}!{y}!{z}!} \\ $$

Answered by Ñï= last updated on 13/Mar/21

Σ ((( 10)),((x,y,z)) )=(1+1+1)^(10) =3^(10)

$$\Sigma\begin{pmatrix}{\:\:\:\mathrm{10}}\\{{x},{y},{z}}\end{pmatrix}=\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{10}} =\mathrm{3}^{\mathrm{10}} \\ $$

Facebook Tweet Pin

for-x-y-z-10-with-x-y-z-N-find-10-x-y-z-

Leave a Reply Cancel reply