Suppose I have a deck with 40 cards.

3 cards type A,

2 cards type B,

3 cards type C,

and the rest from other types.

I'll take 6 cards from this deck. What's the probability that, at the same time, I'll get at least one card of each types A, B and C?

I know that the hypergeometric distribution should be used. I simulated 5000 times on Excel and reached an aproximated result of 0.032 but I couldn't get to this result analytically.