Chapter 7 - Section 7.4 - Probability and Counting Techniques - Exercises - Page 492: 4

$\displaystyle \frac{11}{12}$

$P(E)=\displaystyle \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$ $n(S)=C(10,5)=252$ $E$ = at least one green $E'$ = no greens (AND 5 of the 7 non-greens) $n(E')=C(3,0)\cdot C(7,5)=21$ $P(E')=\displaystyle \frac{21}{252}=\frac{1}{12}$ $P(E)=1-P(E')=\displaystyle \frac{11}{12}$