Question

calcule: A5,4/A4,2=​

Answer 1

$O~arranjo~A_{n,p}~\acute{e}~dado~por~~\dfrac{n!}{n(n-p)!}.\\Assim,~vamos~desenvolver~a~express\tilde{a}o~dada:\\\\\\\dfrac{A_{5,4}}{A_{4,2}}~=~\dfrac{~\dfrac{5!}{(5-4)!}~}{\dfrac{4!}{(4-2)!}}\\\\\\\dfrac{A_{5,4}}{A_{4,2}}~=~\dfrac{~\dfrac{5!}{1!}~}{\dfrac{4!}{2!}}\\\\\\\dfrac{A_{5,4}}{A_{4,2}}~=~\dfrac{~\dfrac{5\cdot4\cdot3\cdot2\cdot1}{1}~}{\dfrac{4\cdot3\cdot2\cdot1}{2\cdot1}}\\\\\\\dfrac{A_{5,4}}{A_{4,2}}~=~\dfrac{~\dfrac{120}{1}~}{\dfrac{24}{2}}$

$\dfrac{A_{5,4}}{A_{4,2}}~=~\dfrac{~120~}{12}\\\\\\\boxed{\dfrac{A_{5,4}}{A_{4,2}}~=~10}$

Resposta:  10