A bag has 4 red marbles, 5 white marbles, and 6 blue marbles.  Three marbles are drawn from the bag (without replacement).  What is the probability that they are all the same color?
We can have all red, all white, or all blue. Thus the answer is  \begin{align*}
&P(\text{all red}) + P(\text{all white}) + P(\text{all blue}) \\
&\qquad = \left(\frac{4}{15}\times\frac{3}{14}\times\frac{2}{13}\right) +\left(\frac{5}{15}\times\frac{4}{14}\times\frac{3}{13}\right) \\
&\qquad\qquad+\left(\frac{6}{15}\times\frac{5}{14}\times\frac{4}{13}\right)=\boxed{\frac{34}{455}}. \end{align*}