Question

Simplifique:assunto:número binominal...
Expliquem passo a passo,por favor?

Answer 1

$\boxed{\boxed{\left(\begin{array}{c}x\\y\end{array}\right)=C_{x,y}=\frac{x!}{y!(x-y)!}}}$

$n!=n*(n-1)*(n-2)*(n-3)*...*3*2*1$

* No desenvolvimento de fatoriais, sempre diminuímos o número anterior em 1 unidade
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$\left(\begin{array}{c}x\\5\end{array}\right)=\frac{x!}{5!(x-5)!}$

$\left(\begin{array}{c}x\\4\end{array}\right)=\frac{x!}{4!(x-4)!}$

$\boxed{\boxed{\frac{\left(\begin{array}{c}x\\5\end{array}\right)}{\left(\begin{array}{c}x\\4\end{array}\right)}=\frac{\frac{x!}{5!(x-5)!}}{\frac{x!}{4!(x-4)!}}}}$
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$\frac{\frac{x!}{5!(x-5)!}}{\frac{x!}{4!(x-4)!}}}=\frac{x!}{5!(x-5)!}*\frac{4!(x-4)!}{x!}\\\\\frac{\frac{x!}{5!(x-5)!}}{\frac{x!}{4!(x-4)!}}}=\frac{4!(x-4)!}{5!(x-5)!}\\\\\frac{\frac{x!}{5!(x-5)!}}{\frac{x!}{4!(x-4)!}}}=\frac{4!(x-4)*(x-5)!}{5*4!(x-5)!}\\\\\frac{\frac{x!}{5!(x-5)!}}{\frac{x!}{4!(x-4)!}}}=\frac{x-4}{5}$


$\boxed{\boxed{\frac{\left(\begin{array}{c}x\\5\end{array}\right)}{\left(\begin{array}{c}x\\4\end{array}\right)}=\frac{x-4}{5}}}$