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=COUNTIF(range, criteria)
Let's begin by counting the number of participants belonging to OSU's fandom.
To begin, what is the range of values that we'll be counting? Those will be the values in column B that represent which school the participant is supporting.
=COUNTIF(B2:B11, criteria)
Next, our criteria is that the cells in B2:B11 equal "OSU", or else we don't want to count them. So, we'll place "OSU" into criteria.
=COUNTIF(B2:B11, "OSU")
Notice how our result is 6...

...and we have 6 OSU values in the table.
To copy this over to the Michigan value in G2, we'll write the same formula except replace "OSU" with "Michigan".
=COUNTIF(B2:B11, "Michigan")

This shows us we had a total of 4 Michigan values in the table.