Question

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 

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

\(B) {{55}({2\over3})^{10}} \) 

\(C){{220}({1\over3})^{12}} \) 

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

Answer 1

The correct answer is A)55/3(2/3)^11 

Explanation::

There are 12 balls and they are identical .

And 3 identical boxes .

\(That \hspace{0.2cm}means \hspace{0.2cm} there \hspace{0.2cm} is \) 

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

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