If you have Excel 2010 or later you can use NETWORKDAYS.INTL function which allows you to customise which days are counted, e.g. the following formula will count Mondays, Wednesdays and Fridays between a start date in A2 and an end date in B2 (inclusive) while excluding holiday dates listed in H2:H10
=NETWORKDAYS.INTL(A2,B2,"0101011",H$2:H$10)
The string "0101011" defines the days to include - 0 is included, 1 is excluded - it starts with Monday
In earlier excel versions you can use this formula for the same result
=SUMPRODUCT((WEEKDAY(ROW(INDIRECT(A2&":"&B2)))={2,4,6})*(COUNTIF(H$2:H$10,ROW(INDIRECT(A2&":"&B2)))=0))
where {2,4,6} defines the weekdays to include (1=Sun through to 7=Sat)