Suppose a middle school gym currently has $50$ students inside: $28$ students are in $7$th grade, and $22$ students are in $8$th grade. The principal decides to randomly select $5$ of these students to represent the school at the school board meeting.
Four of the $5$ students randomly chosen happened to be in the $8$th grade. The principal’s secretary, surprised by this result, uses binomial calculations to find the likelihood of $4$ or more of those $5$ selected students being in the $8$th grade.
Why would it be incorrect to use binomial calculations in this situation?