In how many ways can an answer key for a quiz be written if the quiz contains 5 true-false questions followed by 2 multiples-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:
A) 160  B) 320  C) 480  D) 600  E) 720
There are 2^5 = 32 possibilities for the true-false answers.   However we need to remove two cases for TTTTT and FFFFF.   There are  4*4= 
<gadget id="calculator"> 4*4</gadget>
<output>16</output>
16 possibilities for the multiple choice questions.   The total number of possibilities is  30*16= 
<gadget id="calculator"> 30*16</gadget>
<output>480</output>
480.   The answer is 480.
<result>C</result>
In how many ways can an answer key for a quiz be written if the quiz contains 5 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?