[tex]nP3=\frac{n!}{(n-3)!}[/tex] [tex]17(nP2)=17(\frac{n!}{(n-2)!})[/tex] Therefore we can write the equation as follows: [tex]\frac{n!}{(n-3)!}=17(\frac{n!}{(n-2)!})[/tex] Dividing both sides by n!, we get: [tex]\frac{1}{(n-3)!}=\frac{17}{(n-2)!}[/tex] [tex]\frac{(n-2)!}{(n-3)!}=17[/tex] Therefore n - 2 = 17 and n = 19 The answer is: n = 19
