Select Random Cases from Many Cases?

I am trying to figure out a way to randomly select 1 case/variable out of many. (ex. choosing 1 ball out of 100 balls and doing this over and over etc...). I am trying to randomly select each case everytime. Like a simple random sample or drawing names out of a hat.

I found some instructions on how to do this in SPSS 17, but I need some verification from someone who has more experience in SPSS and stats to verify that this would indeed work and doesn't screw up the statistics of anything.

Here is what I was thinking of using:

2. Then click SAMPLE-->EXACTLY
3. After this you would choose 1 Case from the first _X___ cases.
4. X would represent our total number of cases to choose from, and we could change the total amount as we eliminate through selection, or add to the total number as new FHT/CHC come in.

Also, from the TRANSFORM MENU-->RANDOM NUMBER GENERATOR-->under the Active Generator Initialization, I would click RANDOM.

Please,if someone could verify that this process would indeed work for randomly selecting 1 case out of an x total of cases over and over that would be very helpful! I'm just not completely sure about this as I have limited experience with stats and SPSS!