Question
cation Question 20, 3.1.40 Assuming that no questions are left unanswered, in how many ways can a ten-question true-false quiz be answered? The quiz can be answered in \( \square \) ways.
Ask by Powell Todd. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quiz can be answered in 1024 ways.
Solution
Each question has 2 choices (true or false). Since there are 10 questions and all must be answered, by the multiplication principle the total number of answer combinations is 2 × 2 × ... × 2 (10 times), which equals 2¹⁰ = 1024.
Thus, the quiz can be answered in 1024 ways.
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Simplify this solution The Deep Dive
When answering a true-false quiz, each question has 2 possible answers: true or false. For a ten-question quiz, the total number of ways to answer the quiz can be calculated using the principle of multiplication. This means you take the number of choices (2) for each question and raise it to the power of the total number of questions (10). Thus, you would have: \[ 2^{10} = 1024 \] So, the quiz can be answered in 1024 ways!
