Question

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 5 and the last digit must be odd. How many different codes are​ available? (Note that 0 is considered an even​ number.)

Answer 1

Answer

Since the first digit cannot be 0, it can be any one of the remaining 9 digits in 9 ways.

The second digit can be any one of the 10 digits (0, 1, 2, ……, 9) in 10 ways. [Note that the question has not put restriction that the digits cannot repeat.]

Similarly, the third digit can be any one of the 10 digits (0, 1, 2, ……, 9) in 10 ways.

The last digit has to be odd, i.e., 1, 3, 5, 7, or 9 => 5 possibilities.

Thus, different codes available are: 9 x 10 x 10 x 5 = 4500