SOLUTION: On a 33 question exam, what is the probability of three students answering the same 22 questions correctly and the same 11 questions incorrectly? The exam is a mix of multiple choi

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Question 485138: On a 33 question exam, what is the probability of three students answering the same 22 questions correctly and the same 11 questions incorrectly? The exam is a mix of multiple choice, true /false and fill in the blank.
Answer by richard1234(5390) About Me  (Show Source):
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?