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At a large high school, there are $20$ senior homerooms each with between $20$ and $25$ students. A random sample of $40$ seniors is to be selected as follows.

Each homeroom teacher will be asked to place the names of the students in their homeroom into a box and then randomly select two names. The two students selected from each of the $20$ homerooms will then be combined to form the sample of size $40$.

Will this method result in a simple random sample of seniors at this high school?


No, because the senior homerooms do not all have the same number of students in them.


No, because not each group of $40$ students has the same chance of being selected.


Yes, because each student in each homeroom has an equal chance of being selected.


Yes, because this is a very simple method of random selection.


Yes, because the names are randomly selected in each homeroom.

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