If 12 identical balls are to be placed in 3 identical boxes, then probability that one of boxes cont

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14.Probability

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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 :

A

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

B

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

C

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

D

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

(JEE MAIN-2015)

Solution

$x + y = 9$

$P{ = ^9}{C_3}{\left( {\frac{1}{3}} \right)^3}{\left( {\frac{2}{3}} \right)^9}$

$ = \frac{{12 \times 11 \times 10}}{3} \times \frac{1}{{{3^3}}} \times {\left( {\frac{2}{3}} \right)^9}$

$ = \frac{{220}}{{{3^3}}} \times {\left( {\frac{2}{3}} \right)^9}$

$ = \frac{{55}}{3} \times \frac{{{2^2}}}{{{3^2}}} \times {\left( {\frac{2}{3}} \right)^9}$

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

Standard 11

Mathematics

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