A) 50
B) 100
C) 150
D) 200
Correct Answer: C
Solution :
Let the boxes be marked as \[A,\ B,\ C\]. We have to ensure that no box remains empty and in all five balls have to put in. There will be two possibilities. (i) Any two containing one and \[{{3}^{rd}}\] containing 3. \[A\](1) \[B\](1) \[C\] (3) \[^{5}{{C}_{1}}{{.}^{4}}{{C}_{1}}{{.}^{3}}{{C}_{3}}=5\ .\ 4\ .\ 1=20\]. Since the box containing 3 balls could be any of the three boxes \[A,\ B,\ C\]. Hence the required number is = \[20\times 3=60\]. (ii) Any two containing 2 each and \[{{3}^{rd}}\]containing 1. \[A\](2) \[B\](2) \[C\] (1) \[^{5}{{C}_{2}}{{.}^{3}}{{C}_{2}}{{.}^{1}}{{C}_{1}}=10\times 3\times 1=30\] Since the box containing 1 ball could be any of the three boxes \[A,\ B,\ C\]. Hence the required number is = \[30\times 3=90\]. Hence total number of ways are = \[60+90=150\].
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