A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be 8 and the last digit must be even. How many different codes are available? (Note that 0 is considered an even number) The number of different codes available is (Type a whole number)

To determine how many different access codes are available, let's break it down step by step. 1. The first digit can be any digit from 0 to 9, except for 8. This gives us 9 possible choices (0, 1, 2, 3, 4, 5, 6, 7, 9). 2. The second digit has no restrictions, so there are 10 possible choices (0 through 9). 3. The third digit also has no restrictions, providing another 10 choices. 4. The last digit must be even. The possible even digits are 0, 2, 4, 6, and 8, which gives us 5 choices. Now, we calculate the total number of different codes by multiplying the choices for each digit: Total codes = (choices for first digit) × (choices for second digit) × (choices for third digit) × (choices for last digit) Total codes = 9 × 10 × 10 × 5 = 4500. So, the number of different codes available is 4500.