MySQL multi-level parent selection/join question - sql

Question

I have a hopefully simple MySQL query question which is eluding me at late at night. I'm trying to do a SELECT which counts the number of instances of a set of data (orders) and groups those instances by a value which exists in a parent a couple levels above the order itself.
For example:
CREATE TABLE `so_test`.`categories` (
`id` int(10) unsigned NOT NULL auto_increment,
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=572395 DEFAULT CHARSET=latin1;
CREATE TABLE `so_test`.`product_group` (
`id` int(10) unsigned NOT NULL auto_increment,
`category_id` int(10) unsigned NOT NULL auto_increment,
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=572395 DEFAULT CHARSET=latin1;
CREATE TABLE `so_test`.`products` (
`id` int(10) unsigned NOT NULL auto_increment,
`product_group_id` int(10) unsigned NOT NULL auto_increment,
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=572395 DEFAULT CHARSET=latin1;
CREATE TABLE `so_test`.`orders` (
`id` int(10) unsigned NOT NULL auto_increment,
`product_id` int(10) unsigned NOT NULL auto_increment,
`customer_id` int(10) unsigned NOT NULL auto_increment,
PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=572395 DEFAULT CHARSET=latin1;
What I'm looking to do is something in the neighborhood of:
SELECT count(orders.id), categoryId
FROM orders, categories WHERE
orders.customer_id in (1,2,3) GROUP BY orders.productId.productGroupId.categoryId
Assuming there are 17 orders for products in category 1, 2 orders for products in category 2, and 214 orders for category 3, what I'm hoping to get back is:
count(orders.id), categoryId
============================
17 1
2 2
214 3
If I was trying to group by say product_id I'd be fine..but the two-levels-up portion is throwing me.
Thanks!

Answer 1

Just join them together:
select categoryid, count(orders.id)
from category c
left join product_group pg on pg.category_id = c.id
left join products on p on p.product_group_id = pg.id
left join orders o on o.product_id = p.id
For categories without an order, count(orders.id) will return 0, while count(*) would return one or more, depending on the number of productgroups and products.
An inner join would not count categories without orders at all.