A bag contains 6 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
First, we need to find the total number of ways to draw 3 marbles out of the bag:
$${17 \choose 3} = \frac{17!}{3!14!} = 680$$
Now, we need to find the number of ways to draw 3 green marbles out of the bag:
$${7 \choose 3} = \frac{7!}{3!4!} = 35$$
Finally, we can calculate the probability:
$$ P(\text{all 3 marbles are green}) = \frac{\text{number of ways to draw 3 green marbles}}{\text{total number of possible draws}} = \frac{35}{680} \approx 0.0515 $$
Therefore, the exact probability that all three marbles drawn will be green is approximately 0.0515.