The number of odd numbers having 4 digits can be formed from _{$\text{{1, 2, 3, }\mathrm{.......}\text{, 9} }$} are

Last place can be filled in$5 (1,3,5,7,9)$ ways and the first 3 places can be filled  in ${}^{8}P_3$ ways .

$\therefore The number of ways=5\times {}^{8}P_3=1680$