Question 1205739: A bag contains 10 red marbles, 9 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?
The probability that all the marbles are red is .
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is .
What is the probability that none of the marbles are red?
The probability of picking no red marbles is
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
There are 27 marbles total, of which you are choosing 5. The denominator of the probability fraction in every case is the total number of possible choices, which is C(27,5).
The numerator of the probability fraction in each case is the number of ways of choosing the specified marbles.
First question -- probability that all are red. That means you choose 5 of the 10 red marbles and 0 of the other 17 marbles. Note the "and" means you multiply the numbers of ways.
ANSWER for the first problem: 
For the other problems, you only need to change the expression in the numerator. I'll let you do that; you won't learn anything from the problem if I do all the work for you. You will probably want to use a calculator, as these numbers get rather large.
Here is the calculation for a case different than in your post: find the probability that the 5 marbles are 1 red, 1 white, and 3 blue. The calculation is
As a check when setting up the calculation for any problem like this, note that the numbers in the numerator must match the numbers in the denominator. In the preceding example, 10+9+8=27 and 1+1+3=5.
If you need/want more help with this problem, re-post it, showing whatever work you have done, and one of the tutors here will help you further with it.
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