A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6 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) 160  D) 168  E) 65
The first digit can be filled in 5 ways   For second digit , it can either be 0 or 1   Case 1 -   If second digit is 1 ,Third digit can take 7 values   number of codes = 5 * 1 * 7= 
<gadget id="calculator">5 * 1 * 7</gadget>
<output>35</output>
35   Case 2 -   If second digit is 0,Third digit can take 6 values ( Third digit can't be zero)   number of codes= 5 * 1 * 6= 
<gadget id="calculator">5 * 1 * 6</gadget>
<output>30</output>
30   Total number of codes= 65   Answer 65
<result>E</result>
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6 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?