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

Engineering

Mathematics

Basic Definitions Related to Probability

Question

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

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

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

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

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Consider 12 different balls and 3 different boxes

$∴$ Probability = $\frac{^{12} C_{3} {(2)}^{9}}{3^{12}} = (\frac{12 \times 11 \times 10}{6}) \times \frac{{(2)}^{9}}{(3^{12})} = \frac{55}{3} {(\frac{2}{3})}^{11}$