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Five balls are to be placed in three boxes. Each can hold all the five balls. The number of different ways can we place the balls so that no box remain empty if ____
Colum-I Colum-II
A) Balls and boxes are all different is equal to P) 2
B) Balls are identical but boxes are different is equal to Q) 6
C) Balls are different but boxes are identical is equal to R) 25
D) Balls as well as boxes are identical is equal to S) 50
T) 150

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$A \to Q, B \to T, C \to S, D \to R$

$A \to T, B \to Q, C \to R, D \to P$

$A \to T, B \to Q, C \to P, D \to S$

$A \to T, B \to Q, C \to P, D \to R$

answer is B.

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Detailed Solution

$(A) = 3^{5} - (3 C, 2^{5} - 3 C_{2}) = 150 (B) = (5 - 3 + 2) C_{2} = 6 (C) = \frac{150}{3!} = 25 (D) = 2 (1, 1, 3 a n d 1, 2, 2)$

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