Попробуйте в таком духе:
SELECT T1.Course, T1.Faculty, T1.COUNT(*) AS Counting FROM Base T1 INNER JOIN
(SELECT Course, Faculty, Max(Age) AS Max_Age FROM Base GROUP BY Course, Faculty) T2
ON T1.Course=T2.Course AND T1.Faculty=T2.Faculty AND T1.Age=T2.Max_Age
GROUP BY Course, Faculty