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Question

There are three bags B1, B2, and B3 containing 2 red & 3 white, 5 red & 5 white, 3 red & 2 white balls respectively. A ball is drawn from bag B1 and placed in B2. Then a ball is drawn from bag B2 and placed in B3. Then a ball is drawn from bag B3. The number of ways in which this process can be completed, if same colour balls are used in the first and the second transfers is (assuming all balls are different)

A
30
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B
180
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C
150
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D
25
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Solution

The correct option is B 180Case I: If red colour ball is drawn in the first and the second transfer, then the number of ways = 2C1× 6C1× 6C1=72 Case II: If white colour ball is drawn in the first and the second transfer, then the number of ways = 3C1× 6C1× 6C1=108 ∴ Total the number of ways=72+108=180

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