You can put this solution on YOUR website!
How many students are there, and how many multiple choice, fill-in-the-blank, and free response questions are there?
Intuitively, if there are a reasonable number of students (e.g. <500) the probability of three of them getting the same 22 correct and 11 incorrect is very low. Then again, it depends on the difficulty of the questions. If 22 of them are extremely easy and the other 11 are extremely difficult, the probability might be higher.
However, I am unable to compute the exact probability because that depends on the number of multiple-choice, free response, true/false and the chances of getting those right differ. Also, how does one find the probability of obtaining a free response question correctly?