Question

The access code for a​ car's security system consists of four digits. The first digit cannot be 4 and the last digit must be even. How many different codes are​ available? (Note that 0 is considered an even​ number.)

Answer 1

Out of 10 digits, 5 are even. Even digits are 0, 2, 4, 6, 8

The first digit cannot be 4 so first digit can be selected in 9 ways. There is no restriction on second and third digits so these digit can be selected in 10 ways each. Last digit must be even so it can be selected in 5 ways. That is possible number of 4 digits codes are

9*10*10*5 = 4500

Hence, possible number of codes are 4500.