Random arraylist generation

Question

I sincerely doubt if this is a unique problem, but I have been unable to find or come up with a workable solution. Briefly, I have two arraylists, each containing characters. One has vowels, the other consonants. I need to get three random vowels and seven random consonants to create a new combined arraylist. Then I need to randomly sort that arraylist. No duplicate items are allowed. This final item seems to be my problem, but if there is a more succinct method of performing this operation I'm ready to hear about it.

Hopefully,
colossus1958

P.S. I hope I have this in the right forum, if not please let me know.