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Six students scored better than the remaining seven, and they all had different sequences of guesses.

There’s only one way to get all 5 outcomes wrong (or right, C(5, 0) = C(5, 5) = 1), and only 5 ways to get exactly one outcome wrong (or right, C(5, 1) = C(5, 4) = 5).

So it follows that six of the students got 3 right (C(5, 2) = C(5, 3) = 10) and seven of them got at most 2 right (at least 3 wrong).

This Python program runs in 43ms.

Solution:The sequence is: Tails, Heads, Tails, Heads, Tails.I did a trial with random numbers and reckoned to find that there’s only about a 1-in-2400 probability of this result occurring by chance: six with three right, the other seven with fewer, and no two with the same sequence. Can that be so, or did I make a mistake in the calculation?

Either way, I don’t believe it shows students are good at predicting the future.