On an average, the number of students that choose to study arts subjects at greyin tide university is 17 each year. what is the probability that exactly 13 students will take up arts in the coming year?

Unfortunately, the number of students enrolled is not known.  This must be known to calculate a numerical probability.

Suppose that there are 1000 students at the university.  Then the probability that a given student picked at random is taking an art course is 17/1000, or 0.017.

Hopefully you have a calculator capable of calculating binomial probability (which is what is involved here).

The following function should give you your

binompdf(1000, 0.017, 13) = 0.0657, or roughly 7%.  The probability that 13 out of 1000 students will be taking an arts course during a given year is roughly 7%.