We had a disscussion at work, so tell me what you think.

There are 4 available concert tickets and 10 people applied to get them. If each person cant win more than 1 ticket, what is the probability that you will win a ticket? I say 40% because based on every single possible outcome, 40% win and 60% lose everytime. He says 47.8 or 1/10+1/9+1/8+1/7 but i dont think that's the case here since you would be out of the running if you were pulled on the first or second try etc? Can someone help explain the right answer?

Thank You!

-Tyson Andrews