Subjects set theory

Students Expertise 8A6476

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Students Expertise 8A6476


1. **Stating the problem:** We have 100 students in total. 48 are experts in Ms. Word. 35 are experts in Ms. Excel. 10 are experts in both Ms. Word and Ms. Excel. We need to find how many students are not experts in either Ms. Word or Ms. Excel. 2. **Formula and explanation:** To find the number of students expert in at least one of the two software, we use the principle of inclusion-exclusion: $$\text{Number expert in Word or Excel} = |W| + |E| - |W \cap E|$$ where $|W|=48$, $|E|=35$, and $|W \cap E|=10$. 3. **Calculate the number of students expert in Word or Excel:** $$48 + 35 - 10 = 73$$ 4. **Calculate the number of students not expert in either:** Total students minus those expert in at least one: $$100 - 73 = 27$$ 5. **Answer:** There are **27 students** who are not experts in either Ms. Word or Ms. Excel.