Raffle probability problem - please help!

We run a raffle to raise funds for our Village Hall. Assume we sell 1000 tickets at £1 for a strip of 5 tickets, we don't sell less than a full strip, there are 30 prizes to be won one at a time, you can win more than once if you are lucky enough, and winning tickets are not returned into the ticket 'bucket'. We can do this raffle in two ways; first way is for individual tickets to go in the bucket so there are 1000 tickets in the bucket and 1000 matching tickets out in the audience. One ticket is drawn at a time for each prize. Second way is for strips of 5 tickets to go in the draw bucket so there are 200 strips in the bucket and 200 strips out in the audience. Once a strip wins a prize the whole strip is discarded. My problem is that some folk argue they have a better chance of winning multiple prizes with the single tickets and I cannot find a definitive answer to this and my maths isn't up to it. Obviously if I buy 25 tickets or 5 strips I can in theory win 25 prizes on a ticket scenario and only 5 prizes on a strip scenario but am I more or less likely to win say 3 prizes with strips or tickets. With 30 prizes and 1000 tickets then there's a 30/1000 chance of any one ticket winning the initial prize, and if I have 25 tickets then I have a 30/1000 x 25 = 0.75 chance of winning that prize; with strips it would be 30/200 x 5 = 0.75 so same chance for the first prize. But for a second prize I would have 29/999 x 24 chance = 0.6966 with tickets and 29/199 x 4 chance = 0.5829 with strips. So I have a better chance with tickets? Or is my logic all wrong? And with this logic for a fifth prize the chance with tickets is 0.5481 and with strips it's 0.1236 so a very much better chance with tickets. Or do you know better? Please help me to be sure of my facts.