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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

$$A) {{55\over3}({2\over3})^{11}}$$

$$B) {{55}({2\over3})^{10}}$$

$$C){{220}({1\over3})^{12}}$$

$$D){{22}({1\over3})^{11}}$$

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Explanation::

There are 12 balls and they are identical .

And 3 identical boxes .

$$That \hspace{0.2cm}means \hspace{0.2cm} there \hspace{0.2cm} is$$

$$^{12}C_3 ×( {1\over3})^3 ×({2\over3})^9$$

=$${220×2^9\over3^{12}}={ {55\over3} ({2\over3})^{11} }$$

by Helping Hand (3.2k points)