A history teacher gives a 20 question T-F exam. In how many different ways can the test be answered if the possible answers are T or F, or possibly to leave the answer blank?
I THINK 60 (not sure)
2 choices for each answer gives 2^20 = 1,048,576
including blanks, that's 3 choices for each question, or 3^20 = 3,486,784,401
100
To find the number of different ways the test can be answered, we need to consider three possibilities for each question: answering True (T), answering False (F), or leaving the answer blank (B).
Since each question has three possibilities, we can calculate the total number of different ways to answer the test by using the principle of multiplication. We multiply the number of possibilities for each question by itself for all 20 questions.
Therefore, the number of different ways to answer the 20-question T-F exam is:
3 x 3 x 3 x ... (20 times) = 3^20.
Now, let's calculate the value:
3^20 = 3 x 3 x 3 x ... (20 times) = 3,486,784,401.
So, there are 3,486,784,401 different ways to answer the 20-question T-F exam considering the possibilities of True, False, or leaving the answer blank.