Excel contains a great function that easily counts the number of workdays between two dates, it even allows you to specify holidays that are not counted.
Formula in cell C4:
The image above shows two dates in cell range B5:B6 that acts as holidays in this example.
Formula in cell C8:
NETWORKDAYS.INTL function is available for Excel 2010 and later versions, it allows you to use custom weekends meaning if you want only Sundays to be weekend you can do that.
The string "1101111" means that all days except Wednesdays are weekends (isn't that great?) in the formula above, see row 9 and 10 above.