A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7 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?	Choose the correct option:
A) 144 B) 152 C) 90 D) 168 E) 176
The first digit can be filled in 6 ways   For second digit , it can either be 0 or 1   90ase 1 -   If second digit is 1 ,Third digit can take 8 values   number of codes = 6 * 1 * 8= 
<gadget id="calculator">6 * 1 * 8</gadget>
<output>48</output>
48   90ase 2 -   If second digit is 0,Third digit can take 7 values ( Third digit can't be zero)   number of codes= 6 * 1 * 7= 
<gadget id="calculator">6 * 1 * 7</gadget>
<output>42</output>
42   Total number of codes= 90   Answer 90
<result>C</result>
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7 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?