[tex]\cfrac{A_5^3}{A_4^2} \\\\\\= \cfrac{\cfrac{5!}{2!} }{\cfrac{4!}{2!}} \\\\\\= \cfrac{5!}{2!} \cdot \cfrac{2!}{4!}\\\\\\= \cfrac{5 \cdot 4! \cdot 2}{4! \cdot 2}\\\\= 5[/tex]
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[tex]\cfrac{A_5^3}{A_4^2} \\\\\\= \cfrac{\cfrac{5!}{2!} }{\cfrac{4!}{2!}} \\\\\\= \cfrac{5!}{2!} \cdot \cfrac{2!}{4!}\\\\\\= \cfrac{5 \cdot 4! \cdot 2}{4! \cdot 2}\\\\= 5[/tex]