Questions: 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 9 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.)

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 9 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.)

Transcript text: 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 9 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 $\square$ (Type a whole number.)

Solution

Solution Steps

Step 1: Calculate the number of choices for the first digit

Since the first digit cannot be 9, and assuming the first digit can be from 0 to 9, there are 9 choices for the first digit.

Step 2: Calculate the number of choices for the middle digits (if any)

For each of the middle positions (if n > 2), there are 10 choices (0 to 9) for each digit, resulting in $10^{n-2} = 100$ choices for the middle digits.

Step 3: Calculate the number of choices for the last digit

If the last digit must be even, there are 5 choices (0, 2, 4, 6, 8).

Step 4: Calculate the total number of different codes

The total number of different codes is given by multiplying the number of choices for each position together: $9 \times 100 \times 5 = 4500$.