# Number of possible combinations for answers to this quiz...

• August 27th 2009, 08:25 AM
Neil McCauley
Number of possible combinations for answers to this quiz...
Hi,

I hope I've started this thread in the right section of the forum. I have the following problem. I have created a quiz that consists of 31 questions. Most of the questions have 6 possible answers to choose from, but some have fewer than 6. I'd like to know how many different ways a person could theoretically answer this quiz - that is, how many different combinations of answers are there? Only one answer can be chosen for each of the 31 questions. I'm guessing that the questions that have fewer than 6 available answers to choose from will make a difference to the answer, so here is the full breakdown of how many options are available for the person completing the quiz to choose from for each question.

Q1. 2
Q2. 2
Q3. 6
Q4. 6
Q5. 6
Q6. 2
Q7. 2
Q8. 6
Q9. 6
Q10. 6
Q11. 4
Q12. 4
Q13. 3
Q14. 6
Q15. 6
Q16. 6
Q17. 6
Q18. 6
Q19. 2
Q20. 4
Q21. 2
Q22. 4
Q23. 6
Q24. 6
Q25. 6
Q26. 6
Q27. 4
Q28. 6
Q29. 6
Q30. 6
Q31. 6

The reason I'd like this answer is so I can tell the person who is completing the quiz (which is to be a featured in a book) exactly how unique their collective answers are. Thanks to anyone who can help! (Happy)
• August 27th 2009, 08:37 AM
Plato
Assuming all thirty-one questions are to be answered, then the total number of different ways the test can be answered is simply the product of all thirty-one numbers.
• August 27th 2009, 08:44 AM
Neil McCauley
If I've understood you correctly, you mean add up all of those numbers I listed next to Qs 1-31? In that case the answer would be 149, which seems much too low to be the total number of possible combinations of answers.

Have I missed something?
• August 27th 2009, 08:51 AM
Neil McCauley
Oh...it seems I've revealed the extent of my maths skills by not understanding what 'product' means. So I should multiply each of the numbers listed above together, like this? 2x2x6x6x6 etc. In which case the answer would be, well, astronomical? I make it 1.19805 × 10 to the 20. Does this sound right to anyone?
• August 27th 2009, 09:09 AM
Plato
Lets make it simple. Say we have a four question test.
$\begin{array}{rl}
{Q1} & 2 \\
{Q2} & 4 \\
{Q3} & 2 \\
{Q4} & 6 \\
\end{array}$

There are $2\cdot 4\cdot 2\cdot 6 =96$ ways to answer that test.
• August 27th 2009, 09:27 AM
Neil McCauley
Right...a yes or no would have sufficed. I know you're probably not in the habit of handing out answers to people but in this case I can't see the point in half explaining something to me - a total layman looking for some advice from experts. I do appreciate what you've said though. Now I need to find a way of CONFIRMING that 1.19805 × 10 to the 20 is the right answer. So, to the 31 question test above, there are 1,200 trillion possible combinations of answers. I think.