17.
^{6}\textrm{P}_{r}= P(6,r)=120
\textup{We know that}\;P(n,k) = \frac{n!}{(n-k)!}
\textup{So:}\;120=P(6,r)=\frac{6!}{(6-r)!}
120 = \frac{720}{(6-r)!} \Rightarrow (6-r)! = \frac{720}{120} = 6
\therefore r = 3,\; \textup{because} \;(6-3)! = 3! = 6
And 14 doesn't make any sense. Even...