To find the probability that all three marbles drawn from the bag are red, we first need to calculate the total number of marbles in the bag. The bag contains:
- 6 red marbles
- 8 blue marbles
- 4 green marbles
Calculating the total number of marbles:
\[ \text{Total marbles} = 6 + 8 + 4 = 18 \]
Next, we will calculate the probability of drawing 3 red marbles out of 6 red marbles. The number of ways to choose 3 red marbles from 6 is given by the combination formula \( \binom{n}{k} \), which represents the number of ways to choose \( k \) objects from \( n \) objects without regard to the order of selection.
\[ \text{Ways to choose 3 red marbles from 6} = \binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \]
Next, we need to calculate the total number of ways to choose any 3 marbles from 18 marbles:
\[ \text{Ways to choose 3 marbles from 18} = \binom{18}{3} = \frac{18!}{3!(18-3)!} = \frac{18 \times 17 \times 16}{3 \times 2 \times 1} = 816 \]
Now, the probability that all three marbles drawn will be red is the ratio of the number of favorable outcomes (choosing 3 red marbles) to the total outcomes (choosing any 3 marbles):
\[ P(\text{3 red marbles}) = \frac{\text{Ways to choose 3 red marbles}}{\text{Ways to choose 3 marbles from 18}} = \frac{20}{816} \]
To simplify this fraction, we can divide both the numerator and the denominator by 4:
\[ \frac{20 \div 4}{816 \div 4} = \frac{5}{204} \]
Thus, the exact probability that all three marbles drawn will be red is:
\[ \boxed{\frac{5}{204}} \]