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 five digits. The first digit cannot be zero and the last digit must be odd. How many different codes are available? (Note that 0 is considered an even number.)

(a) - 4,500

(b) - 3,500

(c) - 5,600

(d) - 3,456

45,000 codes

Step-by-step explanation:

We can define that "digits" are defined to symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are a total of ten digits.

The problem indicates that the first digit cannot be zero, this means that there are 9 options in the first digit of the code.

For the second, third and fourth digits of the code there is no restriction, so there are 10 options for each.

For the fifth digit of the code, we can choose any even digit, so we have 5 options.

This means that there is a total of

9 * 10 * 10 * 10 * 5 = 45,000