The examination to qualify for first round of accountancy accreditation is based on a multiple choice
test. Suppose there are 10 questions on the test, each with 4 possible answers, with only one answer
being correct.
Let X be the random variable for number of correct answers for someone who guesses

There are 4 possible guesses for the first, 4 for the second, 4 for the third, and so on.

Since there are 10 questions total, then the total number of possible guesses would be

4^{10}

I would say a binomial distribution.

Each question is independent of the other. Knowing one will not cause you to know another one, or don't know another one.
The probability of getting correct or wrong in each question is the same, 1/4 and 3/4 respectively.
There is a definite number of events, in this case 10.