In how many ways can an answer key for a quiz be written if the quiz contains 4 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) 512
B) 656
C) 740
D) 896
E) 972
There are 2^4 = 16 possibilities for the true-false answers.   However we need to remove two cases for TTTT and FFFF.   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  14*64= 
<gadget id="calculator"> 14*64</gadget>
<output>896</output>
896.   The answer is 896.
<result>D</result>
In how many ways can an answer key for a quiz be written if the quiz contains 4 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?