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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?

A

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

B

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

C

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

D

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

E

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

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