Chapter 3.18, Problem 18.17E

a.

To determine

To prove:The equation $\left(\left(\begin{array}{l}n\\ 4\end{array}\right)\right)=\frac{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}{4!}$ .

b.

To determine

To find:An expression for $\left(\left(\begin{array}{l}n\\ 4\end{array}\right)\right)$ .

c.

To determine

To find:A conjecture for $\left(\left(\begin{array}{l}x\\ k\end{array}\right)\right)$ and $\left(\left(\begin{array}{l}-x\\ k\end{array}\right)\right)$ .

d.

To determine

To find:The value for $\left(\left(\begin{array}{l}1/2\\ k\end{array}\right)\right)$ .