The trigonometry practice exam has 6 questions with the answer A 8 questions with the answer Baby 10 questions with the answer C and 9 questions with the answer D
The number of different answer keys that can be created with the letters above is
A. 2.27 × 10^17
B. 3.82 × 10^19
C. 4.00 × 10^24
D. 8.68 × 10^36
B 10 questions***
Use the excerpt from William Howard Taft's Message to Congress, December 3, 1912 to answer the question.
What result does Taft hope for from the foreign policy he describes in this excerpt? Explain
A. return on American investments
B. the opening of new Asian markets
C. an American voice in Asian politics
D. a widening of the open-door policy
The result that Taft hopes for from the foreign policy he describes in this excerpt is the opening of new Asian markets. He talks about the need to "secure a fair share of the valuable trade of the East", and expresses his hope that American commercial interests will be enhanced by an "expanding commerce with that rich and populous part of the world." Therefore, option B is the correct answer.
To find the number of different answer keys that can be created with the given letters and their respective frequencies, we need to calculate the number of permutations of these letters.
First, let's consider the total number of questions, which is the sum of questions with each answer:
Total questions = 6 + 8 + 10 + 9 = 33
Now, to calculate the number of different answer keys, we need to find the number of permutations of these total questions, considering their order.
The formula for the number of permutations is n! / (n1! * n2! * n3! * ... * nk!), where n is the total number of objects, and n1, n2, n3, ..., nk are the frequencies of each object.
Using this formula, we can calculate the number of permutations as follows:
Number of different answer keys = 33! / (6! * 8! * 10! * 9!)
Now, let's calculate the value:
33! / (6! * 8! * 10! * 9!) = 600805296
Converting the answer to scientific notation, we get:
6.01 × 10^8
None of the given answer choices matches this calculated value. Hence, the correct choice is not among the options provided.