Chapter 5, Problem 42E

To determine

To prove: That The $\left(\begin{array}{c}n\\ n_1{n}_2\mathrm{...}{n}_t\end{array}\right)=\left(\begin{array}{c}n-1\\ n_1-1\mathrm{...}{n}_2\mathrm{...}{n}_t\end{array}\right)+\left(\begin{array}{c}n-1\\ n_1\mathrm{...}{n}_2-1\mathrm{...}{n}_t\end{array}\right)+\mathrm{...}+\left(\begin{array}{c}n-1\\ n_1\mathrm{...}{n}_2\mathrm{...}{n}_t-1\end{array}\right)$ by a combinatorial argument.