Answer
$\displaystyle \frac{1}{2}$
Work Step by Step
$P(E)=\displaystyle \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$
$n(S)=C(10,5)=252$
$E$ = at most one green = (exactly $1$ green) OR (exactly $0$ greens)
n(exactly 1 green)= n(exactly 1 green AND 4 of the other 7)=
$=C(3,1)\cdot C(7,4)=3\cdot 35=105$
n(exactly $0$ greens)=n(exactly $0$ greens AND $5$ of the other 7)
$=C(3,0)\cdot C(7,5)=1\cdot 21=21$
$n(E)=105+21=126$
$P(E)=\displaystyle \frac{126}{252}=\frac{1}{2}$
