Twenty-five people go to daily yoga classes at the same gym, which offers eight classes every day. Each attendee wears either a blue, red, or green shirt to class. Show that on a given day, there is at least one class in which two people are wearing the same color shirt.

Therefore, there is at least one class in which two people are wearing the same color shirt

Step-by-step explanation:

Proof: (By contradiction).

Suppose that, in each of the 8 classes,   no two people wear the same color shirt.

Notice that, if there are 4 people in a class, then at least two of them are wearing the same color shirt

because they can only pick between 3 colors.

Hence the number of people in a class must be at most 3.

Since there are 8 classes, then the total number of attendees is at most 24.

A contradiction. Since the problem says there are 25 people attending yoga classes.

Therefore  there is at least one class in which two people are wearing the same color shirt