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)