Question

Atividade 01
Calcule o valor das frações abaixo:
A) 10!/8!

b) 8!/3! 3!

c) 4! 4! 4!/7!

d) (2n)! / (2n-2)!​

Answer 1

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$\boxed{\begin{array}{l}\tt 01\\\rm A)~\sf\dfrac{10!}{8!}=\dfrac{10\cdot9\cdot\diagup\!\!\!\!\!8!}{\diagup\!\!\!\!\!8!}=90\\\rm B)~\sf\dfrac{8!}{3!\cdot3!}=\dfrac{8\cdot7\cdot\diagdown\!\!\!\!6\cdot5\cdot4\cdot\diagup\!\!\!\!\!3!}{\diagup\!\!\!\!\!3!\cdot\diagdown\!\!\!\!6}=1120\\\rm C)~\sf\dfrac{4!\cdot4!\cdot4!}{7!}=\dfrac{4!\cdot4!\cdot\diagup\!\!\!\!\!4!}{7\cdot6\cdot5\cdot\diagup\!\!\!\!4!}=\dfrac{24\cdot24}{210}\\\sf=\dfrac{96}{35}\end{array}}$

$\large\boxed{\begin{array}{l}\rm D)~\sf\dfrac{(2n)!}{(2n-2)!}=\dfrac{2n\cdot(2n-1)\cdot\diagup\!\!\!\!\!(2n-\diagup\!\!\!\!\!2)!}{\diagup\!\!\!\!\!(2n-\diagup\!\!\!\!\!2)!}\\\sf=2n\cdot(2n-1)\end{array}}$