To determine how many different combinations of outcomes are possible when drawing two balls from a box containing 4 red balls, 3 blue balls, and 2 green balls without replacement, we can use the combination formula.

The total number of balls in the box is:

$4 \text{ (red)} + 3 \text{ (blue)} + 2 \text{ (green)} = 9 \text{ balls}$

The number of ways to choose 2 balls out of 9 is given by the combination formula:

$\text{Number of combinations} = \binom{9}{2} = \frac{9 \times 8}{2 \times 1} = 36$

So, there are 36 different combinations of outcomes possible when two balls are drawn from the box without replacement.

Would you like details on how to solve this, or have any questions?

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Here are 5 related questions to expand your understanding:

1. What is the probability of drawing two red balls from the box?
2. How would the outcome change if the balls were drawn with replacement?
3. What is the probability of drawing one red ball and one blue ball?
4. How many combinations would be possible if three balls were drawn instead of two?
5. What is the probability of drawing two balls of the same color?

Tip: When dealing with problems of combinations and probability, always start by determining the total number of possible outcomes before analyzing specific cases.