Question

At a school with 100​ students, 35 were taking​ Arabic, 39 ​Bulgarian, and 33 Chinese. 19 students take only​ Arabic, 24 take only​ Bulgarian, and 17 take only Chinese. In​ addition, 14 are taking both Arabic and​ Bulgarian, some of whom also take Chinese. How many students are taking all three​ languages? None of these three​ languages?

Answer 1

So there are 7 students taking all languages. To find out how many are taking no languages, take 100 and subtract from it your A, B, C, AB, BC, AC & ABC because none of these values overlap students. You should get 13.

People taking exactly Arabic & Bulgarian (AB)

People taking exactly Bulgarian & Chinese (BC)

People taking exactly Arabic & Chinese (AC)

People taking all three (ABC)