Question
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^ th draw is a white ball, green ball, and blue ball, respectively. If the probability P (W_1 G_2 B_3 )= 2 5 N and the conditional probability P (B_3 W_1 G_2 )= 2 9 , then N equals ________.