A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1,2,3$, let $W _ { i } , G _ { i }$, and $B _ { i }$ denote the events that the ball drawn in the $i ^ { \text {th } }$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P \left( W _ { 1 } \cap G _ { 2 } \cap B _ { 3 } \right) = \frac { 2 } { 5 N }$ and the conditional probability $P \left( B _ { 3 } \mid W _ { 1 } \cap G _ { 2 } \right) = \frac { 2 } { 9 }$, then $N$ equals $\_\_\_\_$ .
A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1,2,3$, let $W _ { i } , G _ { i }$, and $B _ { i }$ denote the events that the ball drawn in the $i ^ { \text {th } }$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P \left( W _ { 1 } \cap G _ { 2 } \cap B _ { 3 } \right) = \frac { 2 } { 5 N }$ and the conditional probability $P \left( B _ { 3 } \mid W _ { 1 } \cap G _ { 2 } \right) = \frac { 2 } { 9 }$, then $N$ equals $\_\_\_\_$ .