You can add a second column with a formula of the form
which will determine if the first character of the cell
A1 is a numeric character, which in your example would correspond to a workday. Workdays will be represented by
1 in the new column, other days by
0. Note that this formula assumes that your workdays always start the field with a number, and free days never do!
You can then sum over this new column to get the total number of workdays.
As mentioned in the comments, you can try to use the function
COUNTIF which in principle allows to count cells with certain characteristics without the need for a temporary column. The problem is that AFAIK you can't use the full flexibility of individual formulas, so I can't come up with a version checking explicitly for cells starting with a numeric character. I found a solution which works for your example though:
which (I think) counts cells whose first character has a smaller ASCII code than the letter "A". Note that this includes a lot of non-letter characters, notable the
Option 3 includes using an array formula, inspired by a Tip of the Day on MrExcel.com:
This needs to be entered as an array formula, i.e. by pressing
Ctrl+Shift+Enter instead of just Enter. This solution is equivalent to the first one I gave, but avoiding the extra column. Note that the extra column still has the advantage that you can manually verify for each day individually that it was classified correctly.