JEE Advanced 2024 Mathematics question on Probability

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 $P(W_1 \cap G_2 \cap B_3) = \dfrac{2}{5N}$ and the conditional probability $P(B_3 \mid W_1 \cap G_2) = \dfrac{2}{9}$, then $N$ equals ______.