If 12 identical balls are to be placed random | vedclass

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Question

Number of elements in sample spa ce $=\mathrm{n}(\mathrm{s})$

$=3^{12}$

If $E$ corresponds to the event that one of the boxes contains exactly $

Vedclass · Accepted Answer

$\frac{{\left( {428} \right){}^{12}{C_3}}}{{{3^{11}}}}$

Vedclass · Answer

Number of elements in sample spa ce $=\mathrm{n}(\mathrm{s})$

$=3^{12}$

If $E$ corresponds to the event that one of the boxes contains exactly $3$ balls then $\mathrm{n}(\mathrm{E})=$

${\,^{12}}{{m{C}}_3} 	imes {\,^3}{{m{C}}_1} 	imes \left[ {{2^9} - 2{m{x}}{\,^9}{{m{C}}_3}} ight] + {\,^2}{{m{C}}_6} 	imes {\,^3}{{m{C}}_1} 	imes {\,^6}{{m{C}}_3}$

required probability $ = \frac{{{m{n}}({m{E}})}}{{{m{n}}({m{s}})}} = \frac{{\left( {428} ight){\,^{12}}{C_3}}}{{{3^{11}}}}$

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

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