In how many ways can an answer key for a quiz be written if the quiz contains 3 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?  Choose the correct choice from the following answers:
A) 164  B) 224  C) 280  D) 384  E) 476
There are 2^3 = 8 possibilities for the true-false answers.   However we need to remove two cases for TTT and FFF.   There are  4*4*4= 
<gadget id="calculator"> 4*4*4</gadget>
<output>64</output>
64 possibilities for the multiple choice questions.   The total number of possibilities is  6*64= 
<gadget id="calculator"> 6*64</gadget>
<output>384</output>
384.   The answer is 384.
<result>D</result>
In how many ways can an answer key for a quiz be written if the quiz contains 3 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?