Probability Question (1 Viewer)

[Ryuuzaki]

At Tristan's school, all students are required to study 3 different electives.
They must choose one language: Greek(Gr), Arabic(A) or French(F),
one Social Science: History(H), Geography(Ge), Legal Studies(L) or Business(B),
and one Technical subject: Computing(C), Design(D) or Technology(T).
How many different elective combinations are there available

I thought it would be 3 x 4 x 3 = 36 but the answer is 12 according to the answer at the back of the textbook?

Lets brute force this and see how many combinations we have...

Grp 1: Gr, A, F
Grp 2: H, Ge, L, B
Grp 3: C, D, T

Combinations:

1. Gr, H, C
2. Gr, H, D
3. Gr, H, T
4. Gr, Ge, C
5. Gr, Ge, D
6. Gr, Ge, T
7. Gr, L, C
8. Gr, L, D
9. Gr, L, T
10. Gr, B, C
11. Gr, B, D
12. Gr, B, T

...

So there, I already have 12 combinations, and I've only done Greek (not Arabic or French yet).

Clearly, the answer is > 12.