Of 500 students, 329 take Economics, 186 Geography, 295 Mathematics; 83 take E and G, 63 G and M, 217 E and M, and everyone takes at least one. How many take all three?

1. Inclusion–exclusion for three sets: $n(E\cup G\cup M)=n(E)+n(G)+n(M)-n(E\cap G)-n(G\cap M)-n(E\cap M)+n(E\cap G\cap M)$. 2. Every student takes at least one subject, so the union is $500$. 3. Substitute: $500=329+186+295-83-63-217+x$. 4. The sums give $810-363=447$, so $500=447+x$. 5. Therefore $x=53$ students take all three subjects. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 5: Sets_