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 sixsix digits. The first digit cannot be 55 and the last digit must be oddodd. How many different codes are​ available? (Note that 0 is considered an even​ number.)

Answer 1

Given Data:

Number consists 6 digits

0, 1 2 3 4 5 6 7 8 9

Given that first digit of the number cannot be 5, from the above list remove 5 so remaining 9 digits in 9 ways

Second digit can be any one of the 10 digits in 10 ways

Third digit can be any one of the 10 digits in 10 ways

Fourth digit can be any one of the 10 digits in 10 ways

Fifth  digit can be any one of the 10 digits in 10 ways

Sixth digit or last digit has to be odd i.e., 1,3,5,7,9 = 5 digits in 5 ways

Different codes are available = 9 * 10 * 10 * 10 * 10 * 5 = 450000

450000 different codes are​ available