Question

In a group of 15 people, 7 read French, 8 read English while 3 of them read none of these two. How many of them read French and English both?

• A. 0
• B. 3
• C. 4
• D. 5
• E. 6

Hint:

Use inclusion–exclusion principle for language problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Total people ($U$) = 15. Those who read at least one language = $15 - 3 = 12$.
Step 2: Detailed Explanation:
Let $F$ be French readers and $E$ be English readers. $n(F) = 7$ $n(E) = 8$ $n(F \cup E) = 12$
Step 3: Calculation:
Using the formula $n(F \cap E) = n(F) + n(E) - n(F \cup E)$: $n(F \cap E) = 7 + 8 - 12$ $n(F \cap E) = 15 - 12 = 3$.
Step 4: Final Answer:
The number of people who read both is 3. Thus, the correct option is (b).