If $5$ distinct balls are placed at random into $5$ cells, then the probability that exactly one cell remains empty is

48 / 125

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12 / 125

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8 / 125

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1 / 125

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Solution

The correct option is D $48 / 125$
Required probability $= \frac{^{5} C_{1} (4^{5} -^{4} C_{1} \cdot 3^{5} +^{4} C_{2} \cdot 2^{5} -^{4} C_{3} \cdot 1^{5})}{5^{5}} = \frac{48}{125}$

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If $\sqrt{5^{n}} = 125, t h e n 5^{n \sqrt{64}}$ =

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If 5 different things are placed at random in 3 different boxes, then the probability of placing them such that no box remains empty is

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