I need something like SUMIF that can return a string

Suppose I have A1:A5, which contain the words "red", "blue", "green", "yellow", and "orange"
In B1:B5, I have 1, 1, 1, 0, and 1, and these values are each set by several steps of formulas where they can only be 1 or 0, and exactly 1 cell in the row is always equal to 0. In C1, I want to get the word in A1:A5 that corresponds with the 0 in B1:B5. So in this case, it would find that B4=0, and then return the contents of A4, which is "yellow".

I tried doing this with C1=SUMIF(B1:B5,0,A1:A5), but this does not work. I have a feeling I'm making this a lot harder than it should be, and SUMIF probably isn't even the right function for this.

A somewhat related question (about SUMIF)... can you use a row for the criteria range and a column for the sum range (assuming it's the same total number of cells)?

For question #2, let me start over. I'm probably asking the wrong question based on faulty assumptions about the correct way to pursue this.

Here's an example where I have colors again, and each color relates to each other color in some way represented by a number (it's meaningless, I just made these up to create an example). What I want to do is, if I know the name of the two colors, I want to be able to get the value from this table where the intersection is (assuming that one color is known to be in the row and the other color is known to be in the column). So if I have a cell B8="red" and I know this means the color along the row B1:F1, and C8="blue and I know this refers to the column A2:A6, I have a cell E8=(some formula) that somehow ends up displaying a value of 1.241.

You can use this formula:

=INDEX($B$2:$F$6,MATCH(C8,$A$2:$A$6,0),MATCH(B8,$B$1:$F$1,0))

when the index range covers two dimensions, the syntax is:

INDEX(table,row,column)

Hope this helps.

Pete