I'm going to agree with @hlsmith and @Dason; it is unclear what the question is actually asking. Is there some variable for which one of 5 categories may occur and you're asking what is the probability of seeing 2 of the first ,1 of the second,0 of the third, 0 of the 4th, and 17 of the 5th category?
My interpretation was an expanding on @Dason's idea, but if you are unsure of the question on your own, I suggest that you ask the professor the correct interpretation first (i.e. is this a single multinomial variable with 5-levels). This will help us avoid guidance that may not be correct given the true intention of the problem.