Example 2.1.1 How many odd numbers with different digits are there between 1000 and 9999?
Solution: In a four-digit number, the unit digit must be an odd number, which can be $1,3,5,7,9$, giving a total of five choices. The highest digit cannot be 0 and cannot be the digit already chosen for the unit place, leaving 8 choices. The other two digits each have 8 and 7 choices respectively. By the multiplication principle, the total number of numbers satisfying the condition is $5 \times 8 \times 8 \times 7=2240$.