Try
=SUMPRODUCT(($A$2:$A$6=1)*($B$2:$B$6=2)*($C$2:$C$6))    =68
       =SUMPRODUCT(($A$2:$A$6=1)*($B$2:$B$6=3)*($C$2:$C$6))    =11
       =SUMPRODUCT(($A$2:$A$6=1)*($B$2:$B$6=4)*($C$2:$C$6))    =14
where 1 is zoneA and 2, 3, 4 is zoneB