Chapter 3.17, Problem 17.30E

a.

To determine

To Prove: That $\left(\begin{array}{c}n\\ abc\end{array}\right)=\left(\begin{array}{l}n\\ a\end{array}\right)\left(\begin{array}{c}n-a\\ b\end{array}\right)$ .

b.

To determine

To Prove: That $\left(\begin{array}{c}n\\ abc\end{array}\right)=\frac{n!}{a!b!c!}$ .

c.

To determine

To Prove: If $a+b+c\ne n$ , then $\left(\begin{array}{c}n\\ abc\end{array}\right)=0$ .