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Standard XII

Mathematics

Combination

There are thr...

Question

There are three bags $B_{1}, B_{2}, and B_{3}$ containing $2$ red & $3$ white, $5$ red & $5$ white, $3$ red & $2$ white balls respectively. A ball is drawn from bag $B_{1}$ and placed in $B_{2}$ . Then a ball is drawn from bag $B_{2}$ and placed in $B_{3}$ . Then a ball is drawn from bag $B_{3}$ . 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)

30

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180

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150

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25

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Solution

The correct option is B $180$
Case I:
If red colour ball is drawn in the first and the second transfer, then the number of ways $=^{2} C_{1} \times^{6} C_{1} \times^{6} C_{1} = 72$

Case II:
If white colour ball is drawn in the first and the second transfer, then the number of ways $=^{3} C_{1} \times^{6} C_{1} \times^{6} C_{1} = 108$

$∴$ Total the number of ways $= 72 + 108 = 180$

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