Flags, enum (C)

I'm not very used to programming with flags, but I think I just found a situation where they'd be useful:

I've got a couple of objects that register themselves as listeners to certain events. What events they register for is dependent on a variable that is sent to them when they are constructed. I think a nice way to do this would be to send bitwise OR connected variables, like such: TAKES_DAMAGE | GRABBABLE | LIQUID, etc. Then, in the constructor, the object can check what flags are set and register it self as listener for the ones that are.

But this is where I get confused. Preferably, the flags would be in an enum. But that is also a problem. If we have got these flags:

enum
{
    TAKES_DAMAGE,/* (0) */
    GRABBABLE, /* (1) */
    LIQUID, /* (2) */
    SOME_OTHER /* (3) */
};

Then sending the flag SOME_OTHER (3) will be the same as sending GRABBABLE | LIQUID, will it not?

How exactly do you deal with this stuff?