Very limited math skills here. I have been trying to search for what kind of equation I would need to solve this and have been stuck.
I need to calculate how many possible combinations there would be for answers if I have 7 questions each with the same 4 answers.
So for example, the 4 answers are 100, 75, 50, 25 to each question, and there are 7 total questions.
How can I calculate the total number of possible combinations for a result where all 7 have been answered?
So a possible answer combination could look like
- 100,75,25,25,50,100,100
Only one answer per question.
Best Answer
Assuming only one answer is correct to each of the questions, there are exactly four ways to answer each of the questions, right? Just pick one of them. Since we have seven questions to answer, it follows that the number of ways to answer all of them is exactly $4^7 = 2^{14} = 16384.$ Hope this helps. :)
P.S.: By the way, if you were allowed to choose any number of answers to the questions, you would have $2^4 - 1 = 15$ ways to answer each of the question (you either choose an answer or you don't, so you have a binary choice for each of the four answers and you cannot not choose any answer at all- hence the $-1$), so there would be $15^7 = 170859375$ ways of answering the questionnaire.