Java get a random value from 3 different enums

I am implementing a simple version of the Cluedo game. There are 3 types of cards in the game, Character, Weapon and Room. Since one card is nothing more than a String (i.e no functionality or information other than the name is stored in a card), I chose not to have a Card interface and each type extends Card. Rather I had three enums in my game which are:

public enum Character {Scarlett, Mustard, White, Green, Peacock, Plum;}
public enum Weapon {Candlestick, Dagger, LeadPipe, Revolver, Rope, Spanner;}
public enum Room {Kitchen, Ballroom, Conservatory, BilliardRoom, Library, Study, Hall;}

However there is one case where three types of cards are put together and dealt evenly to each player of the game. For example, one player may have a hand of 2 Characters, 2 Weapons and 1 Room, another player may have 3 Rooms and 2 Characters, so long the total number of cards are even it doesn't matter what type that is.

And that's why I wonder if there is a way to randomly choose one single value from all three enums in Java?

Or I shouldn't do this three enums thing in the first place? (Badly designed)