The number of red cards in the box, 2/5 of the total number, is 2/5*120 = <<2/5*120=48>>48.
The number of cards that are not red is 120-48 = <<120-48=72>>72.
If 5/9 of the remaining cards are black, then there are 5/9*72 = <<5/9*72=40>>40 black cards in the box.
If the remaining cards are green, then there are 72-40 = <<72-40=32>>32 green cards in the box.
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