First, a little context. Normally, if you have just a couple things you don't want to count, you can use COUNTIFS like this:
But this doesn't scale very well if you have a list of many things, because you'll have to add an additional range/criteria pair to each thing you don't want to count. It would be a lot easier to build a list and pass in a reference to this list as part of the criteria. That's exactly what the formula on this page does. The formula in cell F5 is:
At the core, this formula uses the MATCH function to find cells not equal to "a", "b", or "c" with a reversed configuration like this:
Note the lookup_value and lookup_array are "reversed" from the standard configuration — we provide all values from the named range data (B5:B15) as lookup_values, and provide the values we want to exclude as the lookup_array in the named range exclude (D5:D7). Because we give MATCH more than one lookup_value, we get back more than one result in an array like this:
Essentially, MATCH gives us the position of matching values as a number, and returns #N/A for all other values.
The #N/A results are the ones we're interested in, since they represent values not equal to "a", "b", or "c". Accordingly, we use the ISNA function to force all values to either TRUE or FALSE:
In the resulting array, TRUE values correspond to #N/A errors (values not matched) and FALSE values correspond to the numbers (matched values). Then we use a double negative (--) to coerce TRUE to 1 and FALSE to zero.
The SUMPRODUCT function is designed to multiply and then sum multiple arrays. The resulting array inside SUMPRODUCT looks like this:
With only one array to process, SUMPRODUCT sums and returns a final result, 4.
Note: This is an array formula and using SUMPRODUCT instead of SUM avoids the need to enter the formula with control + shift + enter in legacy Excel.
Count minus match
Another way to count cells not equal to any of several things is to count all values, and subtract matches. You can do this with a formula like this:
Here, COUNTA returns a count of all non-empty cells. The COUNTIF function, given the named range exclude will return three counts, one for each item in the list. SUMPRODUCT adds up the total, and this number is subtracted from the count of all non-empty cells. The final result is the number of cells that do not equal values in exclude.
Literal contains type logic
The formula on this page counts with "equals to" logic. If you need to count cells that do not contain many strings, where contains means a string may appear anywhere in a cell, you'll need a more complex formula.