The number of different codes available

Question

The access code for a car's security system consists of five digits. The first digit cannot be 8 and the last digit must be even. How many different codes are available? (NOTE that 0 is considered an even number.)

Answer 1

1st digit cannot be 8, so there are 9 possibilities (0-7,9)

digis 2 to 4 have 10 possibilities (0-9)

digit 5 must be even, so there are 5 possibilities (0,2,4,6,8)

total no of available codes = 9*10^3*5 = 45000

Answer 2

There is 1 possibility for the first digit (8), 10 possibilities for each of digits 2-4 (0-9) and 5 for the last digit (0, 2, 4, 6, 8). Thus there are 1*10³*5 = 5000 possible combinations.