[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
