The number of odd numbers between 1000 and 10,000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 is

It will be 4 digit number and as it is to be odd the unit place can be filled in 5 ways by any of the 5 odd numbers. Out of remaining 8 we have to arrange 3 in

${ }^8{P}_3$ ways.

$\therefore (8\times 7\times 6)\times 5=1680$

by fundamental theorem.