Bag A contains 4 red and 5 black balls and bag B contains 3 red and 7 black balls. One ball is drawn from bag A and two from bag B. Find the probability that out of 3 balls drawn, two are black and one is red.

Explanation

To solve the problem, we need to find the probability that out of the three balls drawn (one from Bag A and two from Bag B), two are black and one is red. We can break this down into three different cases based on the order of drawing the balls.

### Step 1: Identify the Cases
The three cases for drawing the balls can be:
1. Black (from A), Black (from B), Red (from B) - BBR
2. Black (from B), Red (from A), Black (from B) - BRB
3. Red (from A), Black (from B), Black (from B) - RBB

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