If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :  

  • Option 1)

    \frac{55}{3}\left ( \frac{2}{3} \right )^{11}

  • Option 2)

    55\left ( \frac{2}{3} \right )^{10}

  • Option 3)

    220\left ( \frac{1}{3} \right )^{12}

  • Option 4)

    22\left ( \frac{1}{3} \right )^{11}

 

Answers (1)
V Vakul

As we learnt

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

- wherein

Where n repeated experiment and E occurs r times.

 

n(S)=312

n(E)=\ ^{12}C_{3}.2^{9}

P(E)=\frac{^{12}C_{3}.2^{9}}{3^{12}}=\frac{55}{3}\left(\frac{2}{3} \right )^{11}  


Option 1)

\frac{55}{3}\left ( \frac{2}{3} \right )^{11}

This option is correct

Option 2)

55\left ( \frac{2}{3} \right )^{10}

This option is incorrect

Option 3)

220\left ( \frac{1}{3} \right )^{12}

This option is incorrect

Option 4)

22\left ( \frac{1}{3} \right )^{11}

This option is incorrect

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