Prbability stat question

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You need to break the problem down into it's subsections.

First, how many ways can you get three people from the 15 experienced students? This should look familiar.

15!/12! 3!

Now how many ways can you fill up the rest of the slots (8) from the 25 new students?

25!/17! 8!

The total number of combinations of these two events is the product of those answers, so the chance of getting exactly three experienced students with eight new students is

(15!/12! 3!)(25!/17! 8!)

Now do this for four experienced students and five experienced students, add them together and you have the total number of combinations. Finally, the number of possible combinations for 11 students chosen from 40 is:

40!/(29! 11!)

Divide the sum you found above by the total number of combinations and you get 72.7% which is answer B.