Final answer:
To find out how many 4-digit numbers have only odd digits, we calculate 5 options each for the first, second, third, and fourth digits, resulting in 5^4 or 625 such numbers.
Step-by-step explanation:
To calculate how many 4-digit numbers have only odd digits, we need to consider the available odd digits: 1, 3, 5, 7 and 9. Each place in a 4-digit number can be filled by any of these 5 digits. Starting from the left, we have 5 options for the first digit (it can't be zero), 5 options for the second digit, 5 options for the third digit, and 5 options for the last digit.
Using the fundamental principle of counting, the total number of 4-digit numbers with only odd digits is calculated by multiplying the number of options for each digit position:
- First digit: 5 options
- Second digit: 5 options
- Third digit: 5 options
- Fourth digit: 5 options
The total number of such 4-digit numbers is 5 x 5 x 5 x 5 which equals 625.