To count the number of weekdays, minus holidays for your working days, you can use the NETWORKDAYS function, which has three arguments: Start Date, End Date, and Holidays.
The holidays are usually a range of Holiday dates, but this last argument is optional. If Holidays are not used the formula returns the number of weekdays between the two dates. If there is a Holiday list, then they are subtracted as well.
Here is an example:
The Holiday List is a named range that refers to cells A6:A8 in this example.
The answer in cell C2 is 21 days. Meaning July has 21 working days, which are all the weekdays in July minus the 4th of July, which is a Holiday in the USA.
There is also a NETWORKDAYS.INTL which has four arguments.