Question

There are ? colored balls in a box. The number of red balls is ??, the number of green balls is ?? and the number of blue balls is ?? (?=??+??+??). We want to arrange all the balls in a row. We do it in 3 steps. First, we arrange the red balls, then we arrange the green balls and then we arrange the blue balls.
a) How many possible arrangements are there for the red balls in the first step?
b) How many possible arrangements are there for the green balls in the second step?
c) How many possible arrangements are there for the blue balls in the last step?
d) Use your solutions to a, b and c to determine the number of possible arrangements of all the balls in a row. Try to simplify your result as much as possible.

Answer 1