TITLE: One dimensional subspaces of a 3 dimensional vector space over $\mathbb Z/3\mathbb Z$, multiple choice
QUESTION [6 upvotes]: Let $V$ be a 3-dimentional vector space over the field $F_3=\Bbb Z/3 \Bbb Z$  of $3$ elements.the number of distinct 1 dimentional subspaces of $V$ is 


$13$
$26$
$9$ 
$15$

REPLY [9 votes]: Hint:
If $V_n(q)$ be a vector space of dimension $n$ on a field $F=GF(q)$, the number of all one-dimensional subspace of $V$ will be: $$\frac{q^n-1}{q-1}$$ In fact, all non zero scalar products of $\langle e\rangle\subset V$ generate the same subspaces of dimension one.