jmc

There are three ways to draw two blue marbles and a red one: RBB, BRB, and BBR. Since there are no overlapping outcomes, these are distinct cases and their sum is the total probability that two of the three drawn will be blue. The desired probability therefore is $$\frac{10}{16}\cdot \frac{6}{15}\cdot \frac{5}{14}+\frac{6}{16}\cdot \frac{10}{15}\cdot \frac{5}{14}+\frac{6}{16}\cdot \frac{5}{15}\cdot \frac{10}{14}=\boxed{\frac{15}{56}}.$$