Probability of choosing lottery ticket

Question

There is a lot that contains 2 winning tickets out of 10 pieces. When 10 people draw this lot in order, the probability that the 10th person draws a winning ticket is?

Is this the same as choosing from 9 people, 1 person who gets the winning ticket?

Answer 1

The order of drawing does not matter at all. Imagine lining up the people and lining up the tickets on the table. Now draw from the other end and the last shall be first.

Answer 2

The total possible combinations of 10 lottery tickets with 2 winning and 8 loosing is: $10!/(8!*2!) = 45$
The total combinations of 1 winning ticket being at the end i.e the 10th person getting one is: $9!/8! = 9$
Therefore the probability comes out to be $9/45 = 1/5$