## College Algebra 7th Edition

$\displaystyle \left(\begin{array}{l} 5\\ 0 \end{array}\right)-\left(\begin{array}{l} 5\\ 1 \end{array}\right)+\left(\begin{array}{l} 5\\ 2 \end{array}\right)-\left(\begin{array}{l} 5\\ 3 \end{array}\right)+\left(\begin{array}{l} 5\\ 4 \end{array}\right)-\left(\begin{array}{l} 5\\ 5 \end{array}\right)=0$
We evaluate: $\displaystyle \left(\begin{array}{l} 5\\ 0 \end{array}\right)-\left(\begin{array}{l} 5\\ 1 \end{array}\right)+\left(\begin{array}{l} 5\\ 2 \end{array}\right)-\left(\begin{array}{l} 5\\ 3 \end{array}\right)+\left(\begin{array}{l} 5\\ 4 \end{array}\right)-\left(\begin{array}{l} 5\\ 5 \end{array}\right)=\frac{5!}{0!5!}-\frac{5!}{1!4!}+\frac{5!}{2!3!}-\frac{5!}{3!2!}+\frac{5!}{4!1!}-\frac{5!}{5!0!}=0$ Because all the terms cancel.