A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 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?
Select the correct option:
A) 119	B) 152	C) 160	D) 168	E) 176
The first digit can be filled in 7 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 = 7 * 1 * 9= 
<gadget id="calculator">7 * 1 * 9</gadget>
<output>63</output>
63   Case 2 -   If second digit is 0,Third digit can take 8 values ( Third digit can't be zero)   number of codes= 7 * 1 * 8= 
<gadget id="calculator">7 * 1 * 8</gadget>
<output>56</output>
56   Total number of codes= 119   119nswer 119
<result>A</result>
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 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?