Number of $n-1$-dimensional subspaces of $n$-dimensional space over finite field I got a question with two parts. 
Let $V$ be a $n$-dimensional vector space over $\mathbb{F}_{p}$ - finite field with $p$  elements.
a) How many $1$-dimensional subspaces $V$ has.
b) How many $n-1$-dimensional subspaces $V$ has.
I solved (a) with action of the multiplicative group of $\mathbb{F}_{p}$ on $V$, but I didn't succeed to solve (b) with similar idea..
I still prefer an idea with action of groups.. thanks !

Hint: 
There is a bijection between subspaces of dimension $k$ and $k\times n$ matrices of rank $k$ in reduced row-echelon form.
