Math Problem Statement

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?

Solution

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:

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

Total Groups=3×4×5=60\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.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle

Formulas

Total Groups = (Number of Math Students) × (Number of Experimental Students) × (Number of Humanities Students)

Theorems

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Suitable Grade Level

Grades 5-7