Multiple Choice Exam with 20 Questions. . .

[benderzfloozy]

Hi. I have this problem:

A multiple-choice exam has 20 questions, each with four possible answers, and 10 additional questions, each with five possible answers. How many different answer sheets are possible?

At first, I thought it was a combination problem using the multiplication principle. I did C(20, 4) which yielded 4845 and C(10,5) which gave 252. I multiplied the two together and got 1220940 possible answer sheets total.

For some reason, I'm getting the feeling that this is not correct. If someone could verify this or if I'm wrong, push me in the right direction, would be great. Thanks!

 

[pka]

On a test with 10 questions, each with five possible answers, then there are \(\displaystyle 5^{10}\) possible ways to answer.

 

[benderzfloozy]

Um, this is probably a stupid question, but how is it 5^10? I don't see it. Thanks.

 

[pka]

On a test with 10 questions, each with five possible answers, then there are \(\displaystyle 5^{10}\) possible ways to answer.

Just think about the first question: there are five way to answer.
There are five way to answer the second question.
So there 25 ways to answer there first two questions alone.

There \(\displaystyle 5^{3} = {125}\) ways to answer there first three questions, five for each.

So \(\displaystyle 5^{10}\) ways to answer all ten.