Oracle 11g Release 2

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CREATE TABLE Holidays ( HolidayDates ) AS
SELECT DATE '2018-12-25' FROM DUAL UNION ALL
SELECT DATE '2018-12-31' FROM DUAL;
2 rows affected

CREATE TABLE table_name ( start_date, end_date ) AS
SELECT DATE '2018-12-21', DATE '2018-12-26' FROM DUAL UNION ALL
SELECT DATE '2018-12-28', DATE '2019-01-01' FROM DUAL UNION ALL
SELECT DATE '2019-01-01', DATE '2019-01-07' FROM DUAL;
3 rows affected

SELECT t.*,

       ( TRUNC( end_date, 'IW' ) - TRUNC( start_date, 'IW' ) ) * 5 / 7
       + LEAST( TRUNC( end_date   ) - TRUNC( end_date,   'IW' ) + 1, 5 )
       - LEAST( TRUNC( start_date ) - TRUNC( start_date, 'IW' ), 5 )
       - ( SELECT COUNT(1)
           FROM   holidays
           WHERE  HolidayDates BETWEEN t.start_date AND t.end_date
           -- Exclude any weekend holidays so we don't double count.
           AND    TRUNC( HolidayDates ) - TRUNC( HolidayDates, 'IW' ) <= 5
         )
       AS Num_Week_Days
FROM   table_name t;


START_DATE
END_DATE
NUM_WEEK_DAYS


21-DEC-18
26-DEC-18
3

28-DEC-18
01-JAN-19
2

01-JAN-19
07-JAN-19
5