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Default SumIf formula from one column based on criteria from two other col

Hello,

I am knowledgable how to get a SumIf from one column based one or more
criterias from only one other column. However, now I need to compare criteria
from two different columns and return the SumIf from a third column. I tried
Concantenation, but to no avail and even tried nesting If functions but still
no avail. Can anyone help?

Below is the scenario:

Col A Col B Col C
52 Winter Pink
23 Spring Pink
6 Fall Green
10 Winter Blue
30 Summer Green
10 Fall Blue
5 Spring Green
45 Winter Green
80 Fall Pink
12 Summer Pink
34 Summer Blue

Now how do I return the sum of Col A for all criteria that meets Spring =
Green or Pink + Fall = Green or Pink based on Col's B & C?. And only the sum
of those criterias?
 
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