Final answer:
To find the probability that among the balls drawn there is at least one ball of each color, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. The probability is 16/91.
Step-by-step explanation:
To find the probability that among the balls drawn there is at least one ball of each color, we need to find the total number of favorable outcomes and divide it by the total number of possible outcomes.
There are 3 colors: red, white, and black. We can choose at least one ball of each color in 2 different ways: (1) we choose 1 red, 1 white, and 2 black balls, or (2) we choose 1 red, 2 white, and 1 black balls.
Let's calculate the probability using option 1:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
= (6C1 * 4C1 * 5C2) / (15C4)
= (6 * 4 * 10) / 1365
= 240 / 1365
= 16 / 91
So, the probability that among the balls drawn there is at least one ball of each color is 16/91.