Answer :
Certainly! Let's determine whether the statement about the true/false test makes sense by following these steps:
1. Understand the problem: We have an eleven-item test where each item is a true/false question. We are asked to determine how many possible sets of answers there are.
2. Apply the Fundamental Counting Principle: For each question on the test, there are 2 choices (True or False). This principle helps us calculate the total number of combinations by multiplying the number of choices for each item.
3. Calculate the total combinations:
- For 11 questions, with each having 2 possible answers, the formula to find the total number of answer sets is [tex]\(2^{11}\)[/tex].
- [tex]\(2^{11} = 2048\)[/tex].
4. Compare with the given number: We need to verify if 2048 is more than 2,000.
5. Conclusion:
- Since 2048 is indeed more than 2,000, the statement that there are more than 2,000 possible sets of answers on such a test makes sense.
Thus, the correct answer choice is OD: This statement makes sense because, according to the Fundamental Counting Principle, the number of possible sets of answers on an eleven-item true/false test is 2048, and this value is more than 2,000.
1. Understand the problem: We have an eleven-item test where each item is a true/false question. We are asked to determine how many possible sets of answers there are.
2. Apply the Fundamental Counting Principle: For each question on the test, there are 2 choices (True or False). This principle helps us calculate the total number of combinations by multiplying the number of choices for each item.
3. Calculate the total combinations:
- For 11 questions, with each having 2 possible answers, the formula to find the total number of answer sets is [tex]\(2^{11}\)[/tex].
- [tex]\(2^{11} = 2048\)[/tex].
4. Compare with the given number: We need to verify if 2048 is more than 2,000.
5. Conclusion:
- Since 2048 is indeed more than 2,000, the statement that there are more than 2,000 possible sets of answers on such a test makes sense.
Thus, the correct answer choice is OD: This statement makes sense because, according to the Fundamental Counting Principle, the number of possible sets of answers on an eleven-item true/false test is 2048, and this value is more than 2,000.
