Question

Six differently colored balls (red, blue, green, orange, purple, and white) are placed in a basket. Without looking, three balls are removed. What is the total number of combinations that include a red ball?

Answer 1

\[3\left(\begin{matrix}5 \\ 2\end{matrix}\right) = 30\] since the red ball can be picked first, second or third and each choice has 5 choose 2 choices for the other two balls.