Answer
See below.
Work Step by Step
We know that probability$=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}.$ There are $33$ students in total.
The number of good outcomes is $1$.
If we want to choose $k$ elements out of $n$ disregarding the order, not allowing repetition, we can do this in $_{n}C_k=\frac{n!}{(n-k)!k!}$ ways.
The order doesn't matter here in the set of balls, thus we have to use combinations. Thus the number of all outcomes is: $_{75}C_{5}\cdot_{15}C_{1}=\frac{75!}{(75-5)!5!}\frac{15!}{(15-1)!1!}=258890850$
Hence the probability: $\frac{1}{258890850}=0.00000000386$
