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Default Sumproduct with mulitple criteria containing equals and or's

I need to sum a column only when multiple criteria is met. Example:

Column A is Priority = 1
Column B is type of application = could contain one of the following or all
four (Application and/or Lotus and/or Mainframe and/or Image Dev)
Column C is the number of calls per application = is an amount for each
entry in Column B (Application 20, Lotus 10, Mainframe 10 and Image Dev 10.

In this example all of the types applications will be reported the name,
Applications, so the result I need is:

Priority 1
Applications 50

I have tried multiple sumproduct versions and either get a result of 20 or
zero

How do I mix equals and or conditions in a sumproduct or should I use a
different method.

Any help would be appreciated.

--
Mike
 
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