[tex]_{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
[tex]_{12}P_{3}=\frac{12!}{(12-3)!}=\frac{12!}{9!}=\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{9\times8\times7\times6\times5\times4\times3\times2\times1}=\frac{479,001,600}{362,880}=1,320[/tex]
OR
[tex]_{12}P_{3}=\frac{12!}{(12-3)!}=\frac{12}{9!}=\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{9\times8\times7\times6\times5\times4\times3\times2\times1} = 12\times11\times10 = 1,320[/tex]