Number of terms in $n$ variables over finite field

Number of terms in $n$ variables over finite field

I'm reading a paragraph in book that say:
Let be $\mathbb{F}$ a finite field. For $d>0$ (degree of the system) the
expression $A={\sum_i^{\min(|\mathbb{F}|-1,d)}}$ ${n}\choose{i}$ represent
the number of terms in $n$ variables over finite field. My question is Why
this formula?. For example for $n=3$, $d=2$. I have $A=7$ but for mine
this is wrong because I will be able to form the polynomial:
$a+bx_1+cx_2+dx_3+ex_1^2+fx_2^2+gx_3^2+x_1x_2 + x_2x_3+x_1x_3$ with $10$
terms.