How are race/class combinations unlocked in Mass Effect 3 multiplayer?

This ME3 wiki page has a list of possible race/class combinations, but by default only the human options are available. How are the other races unlocked?

Solution 1:

This might require updating after the game releases, but in the demo, you can get additional race/class unlocks by purchasing "item packs" with credits you earn by playing the game.

In the demo version, there's a "Recruit Pack" that costs 5,000 cr, and a "Veteran Pack" that costs 20,000 cr. Think of these like a pack of cards you might buy for a collectible card game - you'll get a random assortment of several different things, including the possibility of unlocking a new character.