You will learn a lot more if you work these out yourself with our help. Let's try it that way. To do this kind of problem, it is essential to think about what the question means. "We choose 3 balls from a bucket containing balls of 3 colors and all three balls are of a different color." What means is that 1 ball is blue, 1 ball is white, and 1 ball is red. Given that there are 4 blue balls, how many different ways can I choose one of them? How many ways can I choose 1 white ball out of 5 possible choices? So for each single choice of a blue ball, I have how many choices for a white ball? So how many choices do I have overall for 1 blue ball and 1 white ball? Now think about the red ball. How many ways to pick one out of a collection of six? Now for each of the ways to pick a red ball, what have we already determined to be the number of ways to pick one blue ball and one white ball?
Answer as many of those questions as you can. If you can answer all of them, you are one step away from answering 1a.