Weighted Lottery with Unique Output

Hello!

I'm trying to create a weighted lottery with no duplicates to supplement a waitlist for enrollment at a private school.

The formula I'm currently using looks like this in the output column:

=INDEX(A$2:A$9,COUNTIF(C$2:C$9,"<="&RAND())+1)

This works well except for one problem - I need to ensure there are no duplicates in the output of random numbers.

Thank you for your help on this!