Aisle by aisle

Problem

The owner is about to walk the store with the restock sheet in hand, and wants to know what's waiting in each aisle: how many products each category has, and how many of them are out of stock, with the stock at 0. Show the category, then how many products it has, then how many are out of stock. Every category goes on the sheet: one with everything in place isn't left off: it gets a 0.

A hint: if every product had a 1 next to it when it's out of stock and a 0 when it isn't, all that would be left is adding them up.

What it has to return

This is what comes out with the data in the practice database this challenge uses. The column names don’t count, so name yours however you like: what counts is how many there are and the order they come in. Besides this one, the challenge has hidden tests with other data that are revealed when you submit your solution.

You start with this

SELECT category,
  COUNT(*) AS how_many
FROM products
GROUP BY category;