Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^9{\mathrm{C}}_3$ .
Statement-2: The number of ways of choosing any 3 places from 9 different places is ${ }^9{\mathrm{C}}_3$
 

 $$\begin{gathered} \text{ The number of ways of distributing }\mathrm{n}\text{ identical objects among }\mathrm{r}\text{ persons such } \\ \text{ that each person gets at least one object is same as the number of ways of } \\ \text{ selecting }(\mathrm{r}-1)\text{ places out of }(\mathrm{n}-1){\text{ different places, that is }}^{\mathrm{n}-1}{\mathrm{C}}_{\mathrm{r}-1}\text{. } \end{gathered}$$

The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^{n-1}{\mathrm{C}}_{r-1}={ }^9{\mathrm{C}}_3$ .

The number of ways of choosing any 3 places from 9 different places is ${ }^n{\mathrm{C}}_r={ }^9{\mathrm{C}}_3$