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Default Sum column information based on multiple criteria

I've read the posts on using "sumprodut" instead of "sumif", but I'm either
doing something wrong or using "sumproduct" isn't the right tool for what I'm
doing. Here's my problem:
If $A$8:$A$23 = 660010 and if $B$8:$B$23 = "Ideation", sum $C$8:$C$23.
If the value in column A meets my criteria and the value in column C meets
my criteria, I want to find the corresponding cell in column C and add them
together...

Col A Col B Col C
660010 Ideation $5
665511 Ideation $2
660010 Concept $6
660010 Ideation $5

Based on the above information, I would want my formula to return $10, since
the first and last rows contain the correct criteria. I've tried many things
- sumif (which only allows for one criteria), nested if statements, using ifs
and ands....I've been looking at it so hard that my mind has gone blank. Can
anyone help?

Much appreciated!!
 
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