Mathematics

Problem

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) = \frac{2}{5N} \text{ and the conditional probability } P(B_3 | W_1 \cap G_2) = \frac{2}{9},

then

N

equals \_\_\_\_\_\_.

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