How to Include zero-count when joining 3 tables?

I have 3 tables: Vehicle, type and color

Vehicle

id	brand	type_id	color_id
1	Toyota	   1	   2
2	Toyota	   2	   3
3	GMC	       2	   1
4	BMW	       2	   1

Type

id	name
1	Truck
2	Car

Color

id	name
1	White
2	Red
3	Black

I want to get the count of each combination of type and color including 0 values, like this:

type.name	color.name	        count
Truck	      White	              0
Truck	       Red	              1
Truck	      Black	              0
Car	          White	              2
Car	           Red	              0
Car	          Black	              1

I tried this query below

SELECT type.name, color.name, count(vehicle.id) count
FROM vehicle
RIGHT JOIN type on vehicle.type_id = type.id
RIGHT JOIN color on color.id = vehicle.color_id
GROUP BY type.name, color.name

but it doesn't produce zero values:

type.name	color.name	        count
Truck	       Red	              1
Car	          White	              2
Car	          Black	              1

Is there a neat query to achieve the first results?

As mention @jarlh in comments, this can be done using CROSS JOIN :

WITH CTE AS (
  SELECT t.id as type_id, t.name as type_name, c.id as color_id, c.name as color_name
  FROM type t
  CROSS JOIN color c
)
SELECT c.type_name, c.color_name, count(t.color_id) as count
FROM CTE c
LEFT JOIN vehicle t on t.type_id = c.type_id and t.color_id = c.color_id
GROUP BY c.type_name, c.color_name
order by c.type_name desc, c.color_name desc

Or simply :

SELECT t.name as type_name, c.name as color_name, count(v.id) as count
FROM type t
CROSS JOIN color c
LEFT JOIN vehicle v on v.type_id = t.id and v.color_id = c.id
GROUP BY t.name, c.name
order by t.name desc, c.name desc

Results :

type_name	color_name	count
Truck	    White	    0
Truck	    Red	        1
Truck	    Black	    0
Car	        White	    2
Car	        Red	        0 
Car	        Black	    1

Demo here

Here's another way of doing it.<br/>

with record_count as (

select <br>
b.id [typeid], <br>
b.name [typename], <br>
c.id [colorid], <br>
c.name, <br>
[colorname], <br>
count(*) record_count <br>
from vehicle a <br>
left join type b on a.type_id = b.id <br>
left join color c on a.color_id = c.id <br>
group by b.id, b.name, c.id, c.name <br>

) <br>

select a.typename, a.colorname, isnull(b.record_count,0) count <br>
from ( <br>
<br>
select distinct type.id [typeid], type.name [typename], color.id <br> [colorid], color.name [colorname] <br>
from vehicle , type, color <br>

) as a <br>

left join record_count b on a.typeid = b.typeid <br>
and a.colorid = b.colorid <br>