[tex]A_{8,2} = \cfrac{8!}{6!} = 8 \cdot 7 = 56[/tex]

[tex]A_{4,3} = \cfrac{4!}{1!} = 4! = 24[/tex]

[tex]A_{5,3} = \cfrac{5!}{2!} = 5 \cdot 4 \cdot 3 = 60[/tex]

[tex]A_{10,3} = \cfrac{10!}{7!} = 10 \cdot 9 \cdot 8 = 720[/tex]

[tex]A_{9,1} = \cfrac{9!}{8!} = 9[/tex]

[tex]\cfrac{A_{8,2} + A_{4,3} - A_{5,3}}{A_{10,3} - A_{9,1}} \\\\\\= \cfrac{56 + 24 - 60}{720 - 9}\\\\\\= \cfrac{20}{711}[/tex]