An artist is planning on mixing together any number of different colors from her palette. a mixture results as long as the artist combines at least two colors. if the number of possible mixtures is less than 500, what is the greatest number of colors the artist could have in her palette?

If the answer is of the form (nk)(nk) , what is the minimum value of n-k?

If you are trying to calculate, don't bother.

The answer is 1. 

Why, because the answer, i.e (nk)(nk) , will be a number, let us assume that the answer is c, a constant number, which can be written as -

(c1)(c1) = (cc−1)(cc−1)

So, answer is c-(c-1)=1.

Basically any question of this form, will have the answer 1, you even don't have to solve the problem.