Someone has probably already answered this but I don’t know enough math jargon to search properly.

If I have a bag of ten marbles, nine white and one black, the odds of my pulling the black marble is
1:10

Let’s say I pull wrong, which I likely will, and that white marble that I’ve selected gets removed from the bag. Now, my odds of pulling the black is
1:9

Assume I do this a total of nine times, and I’ve pulled out every white marble until ultimately I have the one black marble left.

How would I find out the odds I would pull all the whites out before the one black?

Are my odds essentially
1/10x9x8x7x6x5x4x3x2x1 ?

1:3,628,800 ?

That can’t possibly be right.