Question

In the following exercises, evaluate.
$\text{(a)}\left(\begin{array}{l}7\\ 1\end{array}\right)\text{(b)}\left(\begin{array}{l}4\\ 4\end{array}\right)\text{(c)}\left(\begin{array}{l}3\\ 0\end{array}\right)\text{(d)}\left(\begin{array}{l}10\\ 8\end{array}\right)$

Short answer

(a)$7$

(b)$1$

(c)$1$

(d)$45$

Step-by-step solution

Part (a) Step 1 Given information  

Evaluate$\left(\begin{array}{l}7\\ 1\end{array}\right)$

Part (a) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}7\\ 1\end{array}\right)& =& \frac{7!}{(7-1)!·1!}\\ & =& 7\end{array}$

Part (b) Step 1 Given information  

Evaluate$\left(\begin{array}{l}4\\ 4\end{array}\right)$

Part (b) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}4\\ 4\end{array}\right)& =& \frac{4!}{(4-4)!·0!}\\ & =& 1\end{array}$

Part (c) Step 1 Given information  

Evaluate$\left(\begin{array}{l}3\\ 0\end{array}\right)$

Part (c) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}3\\ 0\end{array}\right)& =& \frac{3!}{(3-0)!·0!}\\ & =& 1\end{array}$

Part (d) Step 1 Given information  

Evaluate$\left(\begin{array}{l}10\\ 8\end{array}\right)$

Part (d) Step 2 Solution 

$\begin{array}{rcl}\left(\begin{array}{l}10\\ 8\end{array}\right)& =& \frac{10!}{(10-8)!·8!}\\ & =& 45\end{array}$