Using The Countifs Function With Three Criteria

Hello Excel Forum Community!
I fear I've hit my Excel knowledge threshold and would appreciate any help/insight you could provide!!

I have a spreadsheet with three columns that I'm trying to scrutinize

First column = drug
Second column = ship date
Third column = courier service type (i.e. overnight, priority overnight)

The spreadsheet has captured all the drugs dispensed within the first quarter of this year.

Here's an example of a formula I'm using:

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What I'd like to do is create a formula which says, 'for every time Betaseron was dispensed on a Friday in this date range and is tied to a priority overnight service type, provide a count'

The formula above only evaluates for two of the three criteria and I'm having a brutal time attempting to incorporate the third

Thanks in advance for your time and attention to this post!!
p.s. It'd probably be helpful if I could attach the spreadsheet, but it contains protected health information. I'm sorry if this makes things more difficult

The only think I can think of it to add a column that uses the function =WEEKDAY(Your Date Cell). This will give you a number between 1 and 7. Then you can use the COUNIFS to check for the value for Friday (default values is 6) in the new column.

Gottoplay and Special-K, thank you both for your time and insight!
I will play around with these functions *crossing my fingers*

Marking this as solved - thanks again for your help