How many different ways can a test be answered if there are 26 questions with the answer options of True, Fals?

How many different ways can a test be answered if there are 26 questions with the answer options of True, False, and Leaving it blank?


I've tried to figure this out and I think I have the right answer, but trying to submit it online it continues to say that it is incorrect.


Also, could you explain how you figured it out.How many different ways can a test be answered if there are 26 questions with the answer options of True, Fals?
The answer is 3^26, or 2,541,865,828,329.





---





To see why, notice that if the test had only 1 question, then there are three possible ways to answer it: Mark the question true, mark it false, or leave it blank.





If the test had two questions, then we know there are 3 ways to mark the first question; and for *each* of these 3, there are 3 ways to mark the second question. That is, we have the following options:





TT, TF, TB


FT, FF, FB


BT, BF, BB





So there are 3 * 3 = 9 ways to answer a test with two questions.





If the test had three questions, then we know there are 9 ways to mark the first two questions. For *each* of these 9 ways, there are 3 ways to mark the third question. That is, we have the following options:





TTT, TTF, TTB


TFT, TFF, TFB


TBT, TBF, TBB


FTT, FTF, FTB


FFT, FFF, FFB


FBT, FBF, FBB


BTT, BTF, BTB


BFT, BFF, BFB


BBT, BBF, BBB





So there are 9 * 3 = 27 ways to answer a test with three questions.





The pattern should be apparent now--for each additional question added to the test, we multiply the number of total ways the test can be answered by 3.





Thus, for a test with 26 questions, we need to multiply 3 by itself 26 times, which gives 3^26.How many different ways can a test be answered if there are 26 questions with the answer options of True, Fals?
This is a simple problem if you know how to do it:


There is 26 questions.


There is three choices for each one(true/false/leave it blank).


You multiply 26 by 3 (26x3).


Your answer is 78 possible choices.
26 questions, 3 choices per question, 26^3 = 17,576