so yaawn, your formula is exactly the same as 50 * 49 * 48 except you also divide by 3 * 2 * 1 = 6, not sure why but then again it's 4:50 AM and I'm fucking tired.
edit: o is it because the order of the 3 cards coming out does not matter? omg ima genius, yes this makes more sense now
edit edit : o cool eugmac said the same thing, I must say this post has been an exercise in pure win on my part.