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 , 1 or 3, 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?	Choose the correct choice from the following answers.
A) 144 B) 142 C) 160 D) 168 E) 176
The first digit can be filled in 8 ways   For second digit , it can either be 0 or 1 or 3   Case 1 -   If second digit is 1 ,Third digit can take 10 values   number of codes = 7 * 1 * 10= 
<gadget id="calculator">7 * 1 * 10</gadget>
<output>70</output>
70   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= 
<gadget id="calculator">8 * 1 * 9</gadget>
<output>72</output>
72   Total number of codes= 142   Answer 142
<result>B</result>
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 , 1 or 3, 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?