Counting rows with multiple criteria

I know this is a silly beginner question, but is there an easy way to count the number of rows in a table which match criteria based on different columns (sort of a countif with multiple criteria). For example, if Column A in a table has "All, Some, None" responses and Column B has "Main, Off" responses, is there an easy way to count the number of rows in which Column A has All and Column B has Off?

Neondiet wrote:
From an intellectual and philosophical view I agree with you. But from a practical view what I really want to do is just use one application for my spreadsheet tasks, not jump back and forth because one sheet I share with MS Windows users, and another with Numbers users, and another with OS X users who don't have Numbers or Excel but do have NeoOffice. Maybe I have to settle for that though.
Yeah... this kind of situation stinks. Its like needing to writing software that will run on both Macs and PCs.
Anyway, I've followed the advise in this forum and resorted to using a hidden column with concatenated values to solve my own problem, though it does seem like a bit of a hack compared to managing a single formula in a single cell. Horses for courses I suppose.
jaxjason has posted a very elegant pivot table like solution that utilizes this technique. See http://www.numberstemplates.com/forums/showthread.php?t=36
Btw, from what I've read on the net to date, SUM (in Excel) with an array formula answers the original authors problem of counting occurrences of values, not SUMPRODUCT; which I believe sums up the contents of cells in a range, if cells in other ranges match specific criteria.
Yes, if you use the '*' (as indicated above) then SUM() is sufficient though SUMPRODUCT() will work as it degenerates to SUM when there is only one argument. If you use two arrays as arguments (like: = SUMPRODUCT((A1:A4="All"), (B1:B4="Off")), then SUMPRODUCT() is necessary. Here's my understanding of how it works (I hope your able to follow my abuse of algebraic techniques):
=SUM((A1:A4="All") * (B1:B4="Off"))
expanding the array expressions...
=SUM((A1="All", A2="All", A3="All", A4="All") * (B1="Off", B2="Off", B3="Off", B4="Off"))
at this point Excel computes the equality expressions, for example...
=SUM((TRUE, FALSE, TRUE, FALSE) * (TRUE, TRUE, FALSE, FALSE))
expanding the array multiplication...
=SUM((TRUE * TRUE, FALSE * TRUE, TRUE * FALSE, FALSE * FALSE))
Excel, apparently, then, when forced to multiply Boolean values, maps TRUE -> 1 and FALSE -> 0...
=SUM((1 * 1, 0 * 1, 1 * 0, 0 * 0))
performing the multiplications...
=SUM((1, 0, 0, 0))
summing...
=1 + 0 + 0 + 0
resulting...
=1
I'm afraid, now, if I continue any further, Yvan will chastise me.

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    November  2011            CompanyC      1234                1234                 1234                 10                    10                    10
    November  2011            CompanyD      1234                1234                 1234                 10                    10                    10
    December  2011            CompanyA      1234                1234                 1234                 10                    10                    10
    December  2011            CompanyB      1234                1234                 1234                 10                    10                    10
    December  2011            CompanyC      1234                1234                 1234                 10                    10                    10
    December  2011            CompanyD      1234                1234                 1234                 10                    10                    10
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