Eliminating Chance Results

I have conducted an experiment in which 3 groups of 20 participants each had 15 multiple choice questions (3 to choose from each time: 1 correct answer and two distractors).
I am interested in the results from one of the groups (they got 147 answers correct out of 300) but need to prove that these 147 selections were not down to chance. I am not sure which tests to run or how to present this information in the correct statistical format. Is anybody please able to advise? TIA


Less is more. Stay pure. Stay poor.
Each question is like a coin toss with a probability of heads of 33%. So it would be expected that they got 33% right. Each question is an independent toss (assumed). So what is the binomial probability of the getting 147 heads on 300 coin tosses.