Pick until you get all black balls

#1
Hi there,
I need a little help on a common but not so documented problem.
I have a bag of 36 balls.
In that bag I have 3 black balls and 33 balls of other colors.
I want to know the probability to pick the 3 black balls
With my basic probability knowledge I can see that the chances of picking the 3 black balls in the 3 first tries are 1/36 * 1/35 * 1/34.
Ok that was easy but now I dont know how to introduce missed pick.
I never put back a ball in the bag.
So, the probability to pick in the 3 first tries is 1/42840 and to pick in 36 tries is 1 if I have the last black ball as the last ball in the bag.
So how to calculate the chance to pick the black balls in 4, 12 or 24 tries ?
 
#3
Not much, my probabilty knowledge is kinda rusty and old ;) Back to school days and theses days are far away.
But I can start to search on that if it's the right direction.