Probability that each student will have a chair to their needs 20% of all students are left handed. A class of size 20 meets in a room with 5 left handed
and 18 right handed chairs. Find the probability that each student will have a chair to
their needs?

What type of distribution is this and how would I go about solving this?
Let $X$ be the number of left-handed students in the class, then (assuming that each student is left- or right-handed independently of the other students) $X$ is a binomial random variable with parameters $p=\frac{1}{5}$ and $n=20$.

Moreover, assuming that the students cooperate with each other, each student will have a suitable chair if and only if $2\leq X\leq 5$.
There are 4 left-handed students and 16 right-handed students. If they sit randomly, there are $\binom{23}{20}$ seating arrangements.

There are $$\binom{5}{4}\binom{18}{15}$$ ways to have students' needs met.

This looks like a hypergeometric distribution

with $N=23, K=5, n = 15, k = 4$