Product of Column Counts in a Single Formula

Hello everyone,

I have data that looks like this:
A 1 Y
B 2 Z
C 3
_-4

I would like to make a formula that returns the product of the column counts (3*4*2 = 24), but I want to do it in a single cell, without having to put counts in each column.

Here is my unsuccessful attempt:

Formula:

=PRODUCT(COUNTA(OFFSET(A1:A4,0,ROW(1:3)-1)))

Can you upload a small data sample sheet (Go Advanced>Manage Attachments). Give a couple examples with expected results. I'm not following

This is probably way too simplistic, but perhaps...
=COUNT(A:A)*COUNT(B:B)*COUNT(C:C)

ChemistB, here is the sample.

Thank you FDibbins. You're right that I am looking that could work for n columns instead of manually entering it.

It's possible that what I'm looking for can't be done, but I've seen array formulas do a lot that I didn't know excel could do, so I'm wondering if there is a way to do this. I tried feeding PRODUCT a list of columns, but when I evaluated the formula, it produced a list of #value errors instead.

Based on your sample file...

This array formula**:

=PRODUCT(SUBTOTAL(3,OFFSET(A1,,COLUMN(A1:C6)-COLUMN(A1),ROWS(A1:C6))))

** array formulas need to be entered using the key
combination of CTRL,SHIFT,ENTER (not just ENTER).
Hold down both the CTRL key and the SHIFT key
then hit ENTER.

Thank you Tony Valko, that works like a charm!

You're welcome. Thanks for the feedback!