\[\boxed{\mathbf{1072}\mathbf{.}}\]
\[1)\ A_{4}^{1} = 4;\]
\[2)\ A_{5}^{1} = 5;\]
\[3)\ A_{5}^{2} = 5 \bullet 4 = 20;\]
\[4)\ A_{4}^{2} = 4 \bullet 3 = 12;\]
\[5)\ A_{7}^{7} = 7 \bullet 6 \bullet 5 \bullet 4 \bullet 3 \bullet 2 \bullet 1 =\]
\[= 5\ 040;\]
\[6)\ A_{6}^{6} = 6 \bullet 5 \bullet 4 \bullet 3 \bullet 2 \bullet 1 = 720;\]
\[7)\ A_{10}^{3} = 10 \bullet 9 \bullet 8 = 720;\]
\[8)\ A_{8}^{3} = 8 \bullet 7 \bullet 6 = 336.\]