Final answer:
To find the number of 5-digit odd numbers that can be made using the given digits, there are 512 options.
Step-by-step explanation:
To find the number of 5-digit odd numbers that can be made using the digits 2, 4, 6, 7, and 9, we need to consider two conditions:
- The last digit must be odd, so it can only be 7 or 9. That gives us 2 options.
- The other four digits can be any of the remaining 4 digits (2, 4, 6, or 9). Each digit can be chosen independently, so we have 4 options for each digit, resulting in 44 = 256 options.
Therefore, the total number of 5-digit odd numbers that can be made is 2 * 256 = 512.