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 Wi,Gi , and Bi denote the events that the ball drawn in the i‌th ‌ draw is a white ball, green ball, and blue ball, respectively, If the probability P(W1∩G2∩B3)=‌

2

5N

and the conditional probability P(B3∣W1∩G2)=‌

2

9

, then N equals ________.