Probability of Selecting Marbles of Different Colors

A bag contains 5 red, 7 blue, and 8 green marbles. You randomly select 3 marbles from the bag without replacement. What is the probability that all three selected marbles are of different colors?

To calculate this, you need to first determine the total number of ways to choose 3 marbles from the total collection and then calculate the number of ways to choose 3 marbles that are all of different colors.

Let the total number of marbles be

$$ 5 + 7 + 8 = 20 $$

So, you need to compute for both total combinations and favorable outcomes.