### Instruction: A bag has 4 red marbles, 5 white marbles, and 6 blue marbles.  Three marbles are drawn from the bag (without replacement).  What is the probability that they are all the same color?### Response: To find the probability of an event, I need to divide the number of favorable outcomes by the number of possible outcomes.
In this case, the event is that the three marbles are all the same color, so I need to count how many ways that can happen and how many ways to draw three marbles in general.
I can use the combination formula to count the number of ways to choose k objects from n objects: C(n,k) = n! / (k! * (n-k)!)
There are three possible colors for the marbles, so I need to consider each one separately.
For red marbles, there are 4 in the bag, and I need to choose 3 of them.
So the number of ways to do that is C(4,3) = 4! / (3! * 1!) = 4
For white marbles, there are 5 in the bag, and I need to choose 3 of them.
So the number of ways to do that is C(5,3) = 5! / (3! * 2!) = 10
For blue marbles, there are 6 in the bag, and I need to choose 3 of them.
So the number of ways to do that is C(6,3) = 6! / (3! * 3!) = 20
The total number of ways to choose three marbles of the same color is 4 + 10 + 20 = 34
Now I need to count the total number of ways to choose three marbles from the bag, regardless of color.
There are 15 marbles in the bag, and I need to choose 3 of them.
So the number of ways to do that is C(15,3) = 15! / (3! * 12!) = 455