We made a group of three out of 3 math students, 4 experimental students and 5 humanities students.  What is the number of fog states that can be exactly one person from each group?

To find the number of groups that can be formed with exactly one person from each group (math, experimental, and humanities), we can use the multiplication principle.

1. **Number of math students:** 3
2. **Number of experimental students:** 4
3. **Number of humanities students:** 5

The total number of groups can be calculated as follows:

\[
\text{Total Groups} = (\text{Number of Math Students}) \times (\text{Number of Experimental Students}) \times (\text{Number of Humanities Students})
\]

\[
\text{Total Groups} = 3 \times 4 \times 5 = 60
\]

Thus, the total number of ways to form a group with exactly one student from each discipline is **60**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would the calculation change if we had different numbers of students in each group?
2. What if we wanted to form a group with two students from one discipline and one from another?
3. Can we apply this concept to larger groups or different scenarios?
4. How would you calculate the number of ways to choose multiple students from each group?
5. What are some real-world applications of this kind of combinatorial calculation?

**Tip:** Always remember to use the multiplication principle for independent choices when forming groups from multiple categories.

We made a group of three out of 3 math students, 4 experimental students and 5 humanities students. What is the number of fog states that can be exactly one person from each group?

Explore how to calculate the number of ways to form a group with exactly one student from each of three categories: math, experimental, and humanities. This example demonstrates the multiplication principle in combinatorics, resulting in a total of 60 unique groups.

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