Question

In the following exercises, evaluate.

(a) $\left(\begin{array}{l}8\\ 1\end{array}\right)$ (b) $\left(\begin{array}{l}10\\ 10\end{array}\right)$ (c) $\left(\begin{array}{l}6\\ 0\end{array}\right)$ (d)$\left(\begin{array}{l}9\\ 3\end{array}\right)$

Short answer

(a)$8$

(b)$1$

(c)$1$

(d)$84$

Step-by-step solution

Part (a) Step 1 Given information  

Evaluate$\left(\begin{array}{l}8\\ 1\end{array}\right)$

Part (a) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}8\\ 1\end{array}\right)& =& \frac{8!}{(8-1)!·1!}\\ & =& 8\end{array}$

Part (b) Step 1 Given information  

Evaluate$\left(\begin{array}{l}10\\ 10\end{array}\right)$

Part (b) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}10\\ 10\end{array}\right)& =& \frac{10!}{(10-10)!·10!}\\ & =& 1\end{array}$

Part (c) Step 1 Given information  

Evaluate$\left(\begin{array}{l}6\\ 0\end{array}\right)$

Part (c) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}6\\ 0\end{array}\right)& =& \frac{6!}{(6-0)!·0!}\\ & =& 1\end{array}$

Part (d) Step 1 Given information  

Evaluate$\left(\begin{array}{l}9\\ 3\end{array}\right)$

Part (d) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}9\\ 3\end{array}\right)& =& \frac{9!}{(9-3)!·3!}\\ & =& 84\end{array}$