A Bag Contains 4 Red Marbles, 3 Green Ones, 3 $\frac { 1 } { 11 }$

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she does not have all green ones.

A) $\frac { 1 } { 11 }$
B) $\frac { 2 } { 33 }$
C) $\frac { 11 } { 12 }$
D) $\frac { 31 } { 33 }$
E) $\frac { 2 } { 5 }$