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