Question

In a group of 33 high school students, 10 take French, 11 take Spanish, and 5 take both languages. How many students of the group take neither French nor Spanish?

a) 7
b) 8
c) 9
d) 10

Answer 1

By using the principle of inclusion-exclusion, we find that there are 17 students in the group who take neither French nor Spanish, after accounting for the number of students taking either language and subtracting those taking both.

Step-by-step explanation:

To answer the question of how many students take neither French nor Spanish, we can use the principle of inclusion-exclusion in set theory. First, we need to account for the total number of students taking either language, then subtract those taking both, and finally subtract this number from the total student count.

• Start with the total number of students taking French (10) and add the number of students taking Spanish (11), which gives us 21.
• Subtract the number of students taking both languages (5), which results in 16 students taking at least one of the languages.
• Then, subtract this from the total number of students (33) to find how many take neither: 33 - 16 = 17.

Therefore, there are 17 students in the group who take neither French nor Spanish.