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Dumb question about count()

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I'm sure I've done this before, but for some reason, my main noodle is drawing 
a blank. Assume we have three tables defined thusly: 

create table classrooms (
id serial unique not null, 
name varchar
); 

create table seats (
classrooms_id integer not null references classrooms(id), 
position varchar
); 

create table students(
classrooms_id integer not null references classrooms(id), 
name varchar
); 

Now, I want to get a result like: 

classroom | students | seats 
101A 	0	25
101B	22	30
102A	11	0
... etc. 

Something somewhat akin to 

select classroom.title, 
	count(students.id) AS students, 
	count(seats.id) AS seats
from classrooms, students, seats
where classrooms.id=students.classrooms_id
and classrooms.id=seats.id 

Except that it counts 0s for seats/students. 

Why can't I recall/find how to do this particular join? 

-Ben 
-- 
"The best way to predict the future is to invent it."
- XEROX PARC slogan, circa 1978

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