Question

Quanto vale (7/0)+ (8/1)+(9/2)+(10+3)?
a)155
b)145
c)160
d)165
e)150

Answer 1

Resposta:

Explicação passo a passo:

Observação:

$0!=1$

$1!=1$

$2!=2\:.\;1=2$

$3!=3\:.\:2\:.\;1=6$

    Fórmula:

$\left(\begin{array}{ccc}n\\\\p\end{array}\right)=\frac{n!}{p!(n-p)!}$

 $\left(\begin{array}{ccc}7\\\\0\end{array}\right)=\frac{7!}{0!.(7-0)!} =\frac{7!}{7!} =1$

 $\left(\begin{array}{ccc}8\\\\1\end{array}\right)=\frac{8!}{1!.(8-1)!} =\frac{8!}{7!} =\frac{8\:.\:7!}{7!} =8$

 $\left(\begin{array}{ccc}9\\\\2\end{array}\right)=\frac{9!}{2!.(9-2)!} =\frac{9!}{2!\:.\:7!} =\frac{9\:.\:8\:.\:7!}{2\:.\:7!} =\frac{72}{2}=36$

 $\left(\begin{array}{ccc}10\\\\3\end{array}\right)=\frac{10!}{3!.(10-3)!} =\frac{10!}{3!\:.\:7!} =\frac{10\;.\:9\:.\:8\:.\:7!}{6\:.\:7!} =\frac{720}{6}=120$

$Agora\:vamos\:somar\:os\:4\:resultados...$

$1+8+36+120=165$

    $Resposta:(d)$