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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?​


The probability of a $7$th grader versus an 8th grader is not $50\%$.


There is not a fixed number of trials.


The selections are not independent.


There are not two outcomes (success/failure).


The sample size is too small to use binomial calculations.

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