Counting DISTINCT over multiple columns in SQL

My database contents

ID CLASS_CODE ROLL_NO NAME
1 IX 1 Jijo K Jose
2 IX 3 James Jacob
3 X 1 Joy Mathew
4 X 2 Sam George
5 IX 2 Miller John
6 X 3 Thomas John

Display values of distinct rows over one column

select distinct(ROLL_NO) from STUDENT;

ROLL_NO  
1
3
2


Count number of distinct rows over one column

select count(distinct(ROLL_NO)) from STUDENT;

count(distinct(ROLL_NO))  
3

Display values of distinct rows over multiple column

select distinct CLASS_CODE, ROLL_NO from STUDENT;

CLASS_CODE ROLL_NO  
IX 1
IX 3
X 1
X 2
IX 2
X 3

Count number of distinct rows over multiple column

select count(*) from (select distinct CLASS_CODE, ROLL_NO from STUDENT) TEMP;

count(*)  
6

 

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