[tex]\dfrac{_nP_3}{_nC_2}=6\\\\\dfrac{\dfrac{n!}{(n-3)!}}{\dfrac{n!}{2!(n-2)!}}=6\\\\\dfrac{n!}{(n-3)!}\cdot \dfrac{2(n-2)!}{n!}=6\\\\2(n-2)=6\\\\2n-4=6\\\\2n=10\\\\n=5[/tex]
