Question

There are fifteen students writing a Statistics exam. What is the probability of correctly

predicting the three students who obtain the highest marks in the exam, in the correct

order, assuming that no student obtains the same mark as any other student?

Answer 1

There are 15! equiprobable permutations and there are 12! of them corresponding to the right guess (first three elements are fixed), so the probability is 12! / 15! = 1 / 2730.