QJEEAdv24Ma38a5: JEE Advanced 2024 Mathematics - Class 12 JEEAdv24Ma38a5 Solution: A bag contains balls out of which 3 balls are white, 6 balls…

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 ________.