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 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.)

The number of different codes available is?

Answer 1

The first digit cannot be zero, so number of possibilities for the first digit = 9

Number of possibilities for the second digit = 10

Number of possibilities for the third digit = 10

Number of possibilities for the fourth digit = 10

The last digit must be odd, so number of possibilities for the last digit = 5

Clearly, all the digits are independent.

Thus the number of different codes available =91010105 = 45000