A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

152.

Explanation:

The first digit can be filled in 8 ways

For second digit, it can either be 0 or 1

Case 1 -

If second digit is 1, Third digit can take 10 values

number of codes = 8 * 1 * 10 = 80

Case 2 -

If second digit is 0, Third digit can take 9 values (Third digit can't be zero)

number of codes = 8 * 1 * 9 = 72

Total number of codes = 152