Indian Institute of Foreign Trade 2009 Solved Paper

All the terms of the expansion ${\left(\mathit{X}+\mathit{Y}+\mathit{Z}\right)}^{30}$ are of the form $\mathit{k}\times {\mathit{X}}^{\mathit{a}}\times {\mathit{Y}}^{\mathit{b}}\times {\mathit{Z}}^{\mathit{c}}\times {\mathit{W}}^{\mathit{d}}$ where a,b,c,d are all positive integers and $\mathit{a}+\mathit{b}+\mathit{c}+\mathit{d}=30$
We need to find number of solutions of above equation and that will be the number of distinct terms in the expansion number of solutions of equation $\mathit{a}+\mathit{b}+\mathit{c}+\mathit{d}=30$ is given by $\left(\mathit{n}+\mathit{r}-1\right){\mathit{C}}_{\mathit{r}-1}$ here $\mathit{n}=30$ and $\mathit{r}=4$
therefore number of solutions $=33{\mathit{C}}_3=5456$
Therefore our answer is Option 'B'