Answer:
6 students are taking all three
20 students are taking none.
Step-by-step explanation:
Please check image attached.
From the total of 33 that are taking Arabic, 14 only take Arabic and 13 take Arabic and Bulgarian (b + d), so the students that take only Arabic and Chinese together is:
a = 33 - 14 - 13 = 6
From the total of 39 that are taking Bulgarian, 19 only take Bulgarian and 13 take Arabic and Bulgarian, so the students that take only Bulgarian and Chinese together is:
c = 39 - 19 - 13 = 7
Now, from the total of 40 that are taking Chinese, 21 only take Chinese, 6 take only Arabic and Chinese and 7 take only Bulgarian and Chinese, so the number of students that take all three languages is:
d = 40 - 21 - 6 - 7 = 6 students
The number of students that take any language is 14 + 19 + 21 + 6 + 7 + 13 = 80 students, so 100 - 80 = 20 students take none of the three languages
