https://file.aiquickdraw.com/mathbot/file/1728265449369boep7yj9.jpg

The problem in the image describes a situation where there are 5 balls in a box, and you are to determine how many different color combinations can be formed when these balls are drawn one by one, without replacement (no return). The question then gives four different options with specific combinations of colors:

1. **2 red balls and 3 white balls**
2. **2 red balls, 2 yellow balls, and 1 white ball**
3. **1 red ball, 1 yellow ball, and 3 white balls**
4. **1 red ball, 1 yellow ball, 1 blue ball, and 2 white balls**

Now let's break down the problem:

Since the question doesn't explicitly list the colors or the exact number of balls for each color, let's assume that the scenario provided refers to combinations of different colors. The goal is to count how many unique sets of color pairs can arise from the process of drawing 5 balls, given different color combinations in each scenario.

### Solution Process

Each option refers to a specific set of combinations of colors (red, yellow, blue, white). To solve the problem, the task would be to evaluate the combinations of these colors for each scenario:

1. **Option A: 2 red balls and 3 white balls**  
   This gives a straightforward combination of exactly 2 red and 3 white balls.
   
2. **Option B: 2 red balls, 2 yellow balls, and 1 white ball**  
   This option involves a total of 5 balls with red, yellow, and white balls, meaning we have a mix of 2 red, 2 yellow, and 1 white.

3. **Option C: 1 red ball, 1 yellow ball, and 3 white balls**  
   The combination has 1 red, 1 yellow, and 3 white balls.

4. **Option D: 1 red ball, 1 yellow ball, 1 blue ball, and 2 white balls**  
   This combination involves a total of 5 balls, with 1 red, 1 yellow, 1 blue, and 2 white.

Given that each of these options forms a distinct color set combination, the number of different possible color pairings is directly related to the structure of each scenario.

Would you like further breakdown on how to approach problems like this or need more clarification on combinations and permutations?

### Expanding from this question:

1. How would the combinations change if the number of balls or the color distribution was altered?
2. What would happen if the drawing process was with replacement (balls put back into the box)?
3. How many ways can you arrange the 5 balls in total for each option?
4. How would you calculate the probability of drawing a specific combination in each scenario?
5. How does the presence of different colors (more than 3 or 4) impact the calculation of possible combinations?

**Tip:** When working with combinations, remember that without replacement (no returning of balls) drastically reduces the number of possible arrangements compared to with replacement (where items are returned).

Dalam sebuah kotak terdapat 5 buah bola yang dapat diambil satu per satu secara berurutan (pengambilan tanpa pengembalian). Berapa banyak pasangan warna yang dapat terjadi jika yang terambil: 
a. 2 bola merah dan 3 bola putih
b. 2 bola merah, 2 bola kuning dan 1 bola putih
c. 1 bola merah, 1 bola kuning dan 3 bola putih
d. 1 bola merah, 1 bola kuning, 1 bola biru dan 2 bola putih

Explore how to solve combinatorics problems where you draw 5 colored balls without replacement. Learn how different combinations of red, yellow, blue, and white balls can be formed in various scenarios. Suitable for high school students learning probability and combinations.

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