China Naming Network - Baby naming - Is it related to the order in which the lottery tickets are not put back?

Is it related to the order in which the lottery tickets are not put back?

What is the probability of the first lottery? 3/ 10

Probability of the second lottery: 3/10 * 2/9+7/10 * 3/9 = 3/10.

Probability of the third lottery: 3/10 * 3/10 *1/8+3/10 * 7/10 * 2/8 * 7/10.

....

...? 3/ 10

Don't write if it's too long ~ ~?