Solve by simulating the problem. You have a 5-question multiple-choice test. Each question has four choices. You don't know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

Here's how you can do the experiment (simulation).

Since each question has four choices, numbered 1,2,3,4.

Then take a coin and throw it twice to represent your answer guess, with

HH=0

HT=1

TH=2

TT=3

Assume the correct answer is {1,1,1,1}, or any other set you decide to have.

Repeat this 5 times to get the 5 answers, and record the "correct" answers.

This constitutes ONE trial. You can repeat the number of trials as you are required to do.

If the number of trials is a large number, you are better off writing a computer program, using Java, Excel, Perl, C, Basic, or any other language of your choice.