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STD 11 - 14. probability — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 14. probability1 Mark
MCQ
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
  • A
    $\frac{4}{{19}}$
  • B
    $\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}$
  • ✓
    $\frac{{\left( {428} \right){}^{12}{C_3}}}{{{3^{11}}}}$
  • D
    $\frac{5}{{19}}$
✓

Answer

Correct option: C.
$\frac{{\left( {428} \right){}^{12}{C_3}}}{{{3^{11}}}}$
c
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 $\mathrm{n}(\mathrm{E})=$

${\,^{12}}{{\rm{C}}_3} \times {\,^3}{{\rm{C}}_1} \times \left[ {{2^9} - 2{\rm{x}}{\,^9}{{\rm{C}}_3}} \right] + {\,^2}{{\rm{C}}_6} \times {\,^3}{{\rm{C}}_1} \times {\,^6}{{\rm{C}}_3}$

required probability $ = \frac{{{\rm{n}}({\rm{E}})}}{{{\rm{n}}({\rm{s}})}} = \frac{{\left( {428} \right){\,^{12}}{C_3}}}{{{3^{11}}}}$

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