Question

Six differently colored balls, (red, blue, green, orange, purple, and write) 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

i've seen this exact question on a practice HS AIMS test...are you from AZ :)

anyway, since you know 1 of the 3 is a red ball, the problem is simply how many ways can you pick 2 balls out of the remaining 5?

5 choose 2
\[_{5}C_{2} = \frac{5!}{2!3!} = \frac{5*4*3!}{2*3!} = \frac{20}{2}=10\]