JEE Advanced 2024 · Paper 2, Mathematics question 9

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 $P(B_3 \mid W_1 \cap G_2) = \dfrac29$, then $N$ equals _____.