Answer
$\displaystyle \frac{7}{9}$
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 least one white
$E'$ = no whites (AND 5 of the 8 nonwhites)
$n(E')=C(2,0)\cdot C(8,5)=56$
$P(E')=\displaystyle \frac{56}{252}=\frac{2}{9}$
$P(E)=1-P(E')=\displaystyle \frac{7}{9}$