If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 ball is $\frac{55}{\lambda }{\left(\frac{2}{3}\right)}^{11}$  then  $\lambda$ = 
 

$$\begin{gathered} \text{ Since }3\text{ boxes are identical, probability of selecting a box is }1/3 \\ \text{ (in which we are to put three balls) } \\ \mathrm{P}=1/3,\mathrm{q}=1-1/3=2/3 \end{gathered}$$
$$\begin{gathered} \text{ Probability that the selected box should contain exactly }3\text{ balls } \\ =\text{ The probability of exactly }3\text{ success in }12\text{ trails } \\ ={12}_{c_3}{\left(\frac{1}{3}\right)}^3\cdot {\left(\frac{2}{3}\right)}^9=\frac{55}{3}{\left(\frac{2}{3}\right)}^{11} \end{gathered}$$