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A history exam features five questions. Three of the questio
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05 Aug 2018, 14:22
05 Aug 2018, 14:22
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Question Stats:
83% (00:51) correct
16% (01:08) wrong based on 42 sessions
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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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256
Re: A history exam features five questions. Three of the questio
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07 Aug 2018, 06:02
07 Aug 2018, 06:02
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Explanation
This question tests the fundamental counting principle, which states that the total number of choices is equal to the product of the independent choices. The five separate test questions means there are five independent choices.
For the three multiple-choice questions there are four options each, whereas for the two true/false questions there are two options each. Multiplying the independent choices yields (4)(4)(4)(2)(2) = 256 different ways to answer the exam.
This question tests the fundamental counting principle, which states that the total number of choices is equal to the product of the independent choices. The five separate test questions means there are five independent choices.
For the three multiple-choice questions there are four options each, whereas for the two true/false questions there are two options each. Multiplying the independent choices yields (4)(4)(4)(2)(2) = 256 different ways to answer the exam.
Re: A history exam features five questions. Three of the questio
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18 Jul 2020, 02:29
18 Jul 2020, 02:29
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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.
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.
