In how many ways can an answer key for a quiz be written if the quiz contains 5 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 answer.
A) 1220	B) 1650	C) 1920	D) 2440	E) 2860
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*4= 
<gadget id="calculator"> 4*4*4</gadget>
<output>64</output>
64 possibilities for the multiple choice questions.   The total number of possibilities is  30*64= 
<gadget id="calculator"> 30*64</gadget>
<output>1_920</output>
1920.   The answer is 1920.
<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 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?