So the probability of getting a match in a single trial is 1/24.
Let X be the random variable number of students who answer all questions correctly.
X ~ Binomial(n = 13, p = 1/24).
You have to calculate . The easy way to do this is to use technology. Using my TI-89 I get 0.0000069655.
Conclusion: It's highly improbable that 6 or more students would get a perfect match by chance.