Exactly Two Red Balls

Choose two of the four red balls and one of the six blue balls.

Divide by the total number of ways to draw three balls from ten.

1. 1. Count favorable draws

   Choose $2$ reds from $4$ and $1$ blue from $6$.

   $$\left(\genfrac{}{}{0ex}{}{4}{2}\right)\left(\genfrac{}{}{0ex}{}{6}{1}\right)=6\times 6=36$$

2. 2. Divide by total draws

   There are $\left(\genfrac{}{}{0ex}{}{10}{3}\right)=120$ equally likely draws.

   $$P=\frac{36}{120}=\frac{3}{10}$$

Answer: 3/10