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 can not be the same ?
"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 = 64 possibilities for the multiple choice questions . the total number of possibilities is 30 * 64 = 1920 . the answer is c ."
multiply(subtract(power(3, 5), 3), multiply(4, 4))