MySQL多对多关系计数查询

我有三张桌子

|TYPE      |  |REL_TABLE  |  |PRODUCT    |  
|----------|  |-----------|  |-----------|
|Id        |  |Id         |  |Id         |
|Title     |  |TypeId     |  |Name       | 
|CategoryID|  |ProductId  |  

如您所见，关系为TYPE.id->REL_TABLE.TypeID和PRODUCT.id->REL_TABLE.ProductId

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我需要的是CategoryID和产品数量。每个CategoryID的名称

只需加入

和
计数
结果：

   SELECT t.CategoryID,
          COUNT(*)
    FROM TYPE as t
    LEFT JOIN REL_TABLE as r on t.Id = r.TypeId
         JOIN PRODUCT as p on p.id = r.ProductId
GROUP BY t.CategoryID

简单的
join and count
将与
groupby

select t.categoryid, count(p.name)
from type t inner join rel_table rt on
t.id=rt.typeid inner join product p on
rt.productid=p.id
group by t.categoryid