Fluke, but I just happened to look into it this morning!
What you actually want is multiple-condition formula. If you seach Excel
Help under "Sum", there is a great explanation of how to Sum using multiple
conditions. I do not know why the multiple-condition formula option does not
show when you seach "Count", but it does not.
Basically, the key difference is that you have to use an array formula
(another thing I learned this morning). The most important thing to remember
with an array formula is to use brace brackets {} around the entire formula.
You do this by either manually entering them, or by holding CTRL-SHIFT-ENTER
after you finish typing the formula.
The formula you use should look like this:
{=COUNT(IF(($B$4:$B$8=$A24)*($E$4:$E$8=B$20),$C$4:$C$8))}
Where A24 is the first condition you want met; B4:B8 is the column in which
you want this condition to be found; B20 is the second condition you want
met; E4: E8 is the column you want this condition to be found; C4:C8 is the
column you want counted.
Some items of note: I used reference cells, but if you want the condition to
be a word, you can just type in "Apples" instead of A24 or B20. Also, I have
found the exact column to be counted (C4:C8) to be somewhat irrelevant so
long as it is any column in your array of data.
Good luck!