Count holidays between two dates

This formula uses two expressions in a single array inside the SUMPRODUCT function.

The first expression tests every holiday date to see if it's greater than or equal to the start date in F5:

(B4:B12>=F5)

This returns an array of TRUE/FALSE values like this:

{FALSE;FALSE;FALSE;FALSE;TRUE;TRUE;TRUE;TRUE;TRUE}

The second expression tests every holiday date to see if it's less than or equal to the end date in F6:

(B4:B12<=F6)

which returns an array of TRUE/FALSE values like this:

{TRUE;TRUE;TRUE;TRUE;TRUE;TRUE;TRUE;TRUE;FALSE}

The multiplication of these two arrays automatically coerces the TRUE/FALSE values to ones and zeros, resulting in arrays that look like this:

=SUMPRODUCT(({0;0;0;0;1;1;1;1;1})*({1;1;1;1;1;1;1;1;0}))

After multiplication, we have just one array like this:

=SUMPRODUCT({0;0;0;0;1;1;1;1;0})

Finally, SUMPRODUCT sums the items in the array and returns 4.

Holidays on weekdays only

To count holidays that occur on weekdays only (Mon-Fri), you can extend the formula like this:

=SUMPRODUCT((rng>=F5)*(rng<=F6)*(WEEKDAY(rng,2)<6))

where rng is a range containing holiday dates.