A history exam features five questions. Three of the questions are multiple-choice with four options each. The other two questions are true or false. If Caroline selects one answer for every question, how many different ways can she answer the exam?


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Sandy
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I understand the counting method. However, is there a reason we do not account for the order of the 5 questions? What part of the question insinuates this? Thanks!

My initial thoughts were a four-step process.

Step 1: # of possibilities for 3 multiple-choice questions: 4 * 4 * 4 = 64
Step 2: # of possibilities for 2 true-false questions: 2 * 2 = 4
Step 3:# of possibilities for the arrangement of the 5 questions where 3 multiple choice and 2 true-false: (5*4*3*2*1)/(3!)(2!) = 10
Step 4: Multiply them all together for 64*4*10 = 2560.