Let 9 distinct balls be distributed among 4 boxes,

Question:

Let 9 distinct balls be distributed among 4 boxes, $B_{1}, B_{2}, B_{3}$ and $B_{4}$. If the probability than $B_{3}$

contains exactly 3 balls is $\mathrm{k}\left(\frac{3}{4}\right)^{9}$ then $\mathrm{k}$ lies in the

set:

  1. $\{x \in \mathbf{R}:|x-3|<1\}$

  2. $\{x \in \mathbf{R}:|x-2| \leq 1\}$

  3. $\{x \in \mathbf{R}:|x-1|<1\}$

  4. $\{x \in \mathbf{R}:|x-5| \leq 1\}$


Correct Option: , 2

Solution:

required probability $=\frac{{ }^{9} \mathrm{C}_{3} \cdot 3^{6}}{4^{9}}$

$=\frac{{ }^{9} \mathrm{C}_{3}}{27} \cdot\left(\frac{3}{4}\right)^{9}$

$=\frac{28}{9} \cdot\left(\frac{3}{4}\right)^{9} \Rightarrow \mathrm{k}=\frac{28}{9}$

Which satisfies $|x-3|<1$

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