.
The total number of all possible sextuples of 300 marbles is the number of combinations of 300 marbles taken 6 at a time
= = 962822846700.
The number of all different triples of 30 black marbles is
= = 4060.
The number of all different triples of 300-30 = 270 not-black marbles is
= = 3244140.
The probability under the problem's question is
P = = 0.01368 (rounded). ANSWER
Solved.
------------------
To see many other similar (and different) problems solved, look into the lesson
- Elementary Probability problems related to combinations
in this site.