A bag contains two red marbles, three green ones, one lavender one, four yellows, and three orange marbles.
How many sets of four marbles include one of each color other than lavender?

We are asked to determine how many sets of four marbles from a collection contain one red marble, one green marble, one yellow marble, and one orange marble, excluding lavender.

The marbles in the bag are distributed as follows:

- 2 red marbles
- 3 green marbles
- 1 lavender marble
- 4 yellow marbles
- 3 orange marbles

Since we need one marble from each of the colors red, green, yellow, and orange (excluding lavender), we can compute the number of ways to pick one marble from each color:

1. **Red Marbles**: We can choose **1 red marble** from 2 available, which gives us 2 choices.
2. **Green Marbles**: We can choose **1 green marble** from 3 available, which gives us 3 choices.
3. **Yellow Marbles**: We can choose **1 yellow marble** from 4 available, which gives us 4 choices.
4. **Orange Marbles**: We can choose **1 orange marble** from 3 available, which gives us 3 choices.

Now, the total number of possible sets is the product of these choices:

\[
2 \times 3 \times 4 \times 3 = 72
\]

Thus, there are **72 sets** of four marbles that include one red, one green, one yellow, and one orange marble.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the answer change if we included the lavender marble?
2. What if we needed to select 2 red marbles and 2 green marbles?
3. What if we had more colors to choose from?
4. How would the answer change if we wanted sets of 3 marbles instead of 4?
5. How many total sets of 4 marbles can be made without restrictions?

**Tip**: When dealing with combinations, always think about whether repetition is allowed and how each choice affects the total number of possibilities.

A bag contains two red marbles, three green ones, one lavender one, four yellows, and three orange marbles. How many sets of four marbles include one of each color other than lavender?

Learn how to solve a combinatorial problem involving marbles of different colors. This problem covers key concepts in combinatorics, such as the multiplication principle and the fundamental principle of counting, making it ideal for students in Grades 9-11.

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