DanaJ wrote:0! = 1 because some guys interested in math thought they should just have that rule a long time ago (we call it a convention in RO, but I'm not sure this is the correct translation for the word)... I don't know if there is an explanation here, you just have to take it as it is... Kindda like the weight of a kilo/pound or the volume of a liter...

You can think of the relation 0! = 1 as a mathematical convention (and yes, convention is the word mathematicians use to describe something that's held true simply by common agreement - e.g. the fact that 1 is not prime is essentially a convention, though a handful of 'eccentric' mathematicians think it ought to be granted prime status). Still, there are good reasons why 0! should equal 1. For example, if you want to work out, using the formula, what 7C7 is equal to, you get:

7!
7! 0!

and since this should be equal to 1 (there's only one set of 7 you can choose from a group of 7), then 0! must be equal to 1.

And 0^0 (which you'll never need to worry about on the GMAT) is undefined, because, if you think about what it 'should' be equal to, you arrive at different answers. If k is not zero, 0^k = 0 for all numbers k, while k^0 = 1 for all numbers k. So should 0^0 = 0, or should it be 1?

In some applications, 0^0 is accepted to be equal to 1, but for GMAT purposes, it's not defined. I've never seen a question where you'd need to know that, however.