excel nested if multiple logical tests

I have read other threads on this topic, however I found no answers. I have three colums, of which I want to test column a and b and if true I want the som of the results in colum c.

         a      b      c
  1     ba     za       2
  2     ba     az       2
  3     ca     za       2
  4     ca     az       2 
  5     ba     za       2

I want to find the sum if column a = ba and column b = za. So in this example the sum of those would be 4. This is the Excel forumala I have, however it keeps giving the result of 0.

This formula is a nested if.

=Sum(IF(And((a1:a5="ba");b1:b5="za");c1:c5;0))

Can someone please help me with finding the correct formula? I have been breaking my head about this particular formula.

I have been using excel for a while now, and quite got the hang of all the formulas, however this is the only problem I could not wrap my head around.