So it seems you meant to ask: how many different basis for are there in the set of all vectors all of whose coordinates are only 0 or 1...right?

Then your set has 8 elements (the vector (0,0,0) also belongs to it), but certainly you can make it with the 7 vectors you wrote down since you want 3 lin. ind. vectors.

Now observe that ANY two different vectors from these 7 ones are lin. independent (why?), so you need:

(1) find out how many basis are there for any two fixed elements in your set, and then

(2) for each set with three elements as above you have to find all the possible orderings of the vectors , since a basis in is NOT only three lin. ind. vectors but in fact three ORDERED lin. ind. vectors, i.e.: the basis is not the same as the basis , though these two, as SETS, are identical...

Tonio