So, here is how you would do this in a basic PivotTable:
I've created an sample data set like in your example
Now, go to your Insert menu and click PivotTable
Select the cell range for the PivotTable and click OK
You now have a PivotTable in a new tab:
Check Schools and Details to add them to your PivotTable
Now move Details from the Row Labels block to the Column Labels block, and drag another instance of Details to the Values block. The default value is count.
It is really worth it to learn how to effectively use PivotTables. I use these regularly to very quickly compare hundreds of thousands of rows and over a hundred columns of data, and it's so easy to manipulate the results to meet your needs, or create a PivotChart from the data. Our executive team loves how the charts and tables look when I put together a report for them.