Actually, if each pack contains 12 cups and you purchase 9 packs, you will have a total of 9 * 12 = 108 cups. Therefore, you will have more than enough cups for all 100 participants.

Yes, you are correct. With 9 packs, each containing 12 cups, you will indeed have a total of 108 cups. This will be more than enough to provide each of the 100 participants with a cup. You will even have some extra cups remaining.