1. **Problem:** Students are classified by gender (male or female), status (regular or irregular), and field of specialization (mathematics, physics, business, or languages). Find all possible classifications and the total number of classifications. 2. **Formula:** Use the multiplication principle for counting: If there are $n$ ways to do one thing and $m$ ways to do another, then there are $n \times m$ ways to do both. 3. **Step 1:** Identify the number of options for each category: - Gender: 2 (male, female) - Status: 2 (regular, irregular) - Field: 4 (mathematics, physics, business, languages) 4. **Step 2:** Calculate total classifications: $$\text{Total} = 2 \times 2 \times 4 = 16$$ 5. **Step 3:** Explanation: Each choice is independent, so multiply the number of options in each category to get all possible combinations. 6. **Step 4:** Tree diagram (conceptual): - Start with Gender (2 branches) - From each Gender branch, split into Status (2 branches) - From each Status branch, split into Field (4 branches) - Total leaves = $2 \times 2 \times 4 = 16$ **Final answer:** There are 16 possible classifications of students.