How many 4 digit numbers can you build if the number must be odd odd digits can be repeated and even digits cannot be repeated?

Answer 1

To form a 4-digit odd number, the last digit must be one of the odd digits (1, 3, 5, 7, 9), giving us 5 choices. For the first three digits, we can use odd digits freely (repeating allowed), giving us 5 choices for the first digit and 5 choices for the second digit. The third digit must be an even digit (0, 2, 4, 6, 8), but cannot repeat; therefore, we have 5 choices for the first digit and 4 choices for the second digit. Thus, the total number of valid 4-digit odd numbers is calculated as (5 \times 5 \times 5 \times 5 = 625).