Three cards are chosen at random from a standard 52-card deck.  What is the probability that they are not all the same color?
We can find the probability they are all same color, then subtract that from 1. There are 26 cards of each color, so 3 of them can be selected in $\binom{26}{3}$ ways, and of course there are 2 colors.  So the answer is \[1-2\frac{\binom{26}{3}}{\binom{52}{3}}=\boxed{\frac{13}{17}}.\]