There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose.

In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?

Assume that once each marble is chosen, it is not returned to the bag.