#### Answer

a) The value of $ nCr $ for $ n=8$ and $ r=3$ is $\underline{56}$ and is verified.
b) The value of $ nCr $ for $ n=7$ and $ r=2$ is $\underline{21}$ and is verified
c) The value of $ nCr $ for $ n=12$ and $ r=1$ is $\underline{12}$ and is verified
d)The value of $ nCr $ for $ n=11$ and $ r=1$ is $\underline{11}$ and is verified
e)The value of $ nCr $ for $ n=6$ and $ r=6$ is $\underline{1}$ and is verified
f)The value of $ nCr $ for $ n=15$ and $ r=2$ is $\underline{105}$ and is verified
g)The value of $ nCr $ for $ n=100$ and $ r=2$ is $\underline{4,950}$ and is verified
h)The value of $ nCr $ for $ n=100$ and $ r=98$ is $\underline{4,950}$ and is verified

#### Work Step by Step

(a)
Obtain the value of $\left( \begin{align}
& 8 \\
& 3 \\
\end{align} \right)$ as follows:
$\begin{align}
& 8\text{ }nCr\text{ 3 } \\
& \text{ 56} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 8 \\
& 3 \\
\end{align} \right)=56$ and is the same as one obtained before.
(b)
The value of $\left( \begin{align}
& 7 \\
& 2 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& 7\text{ }nCr\text{ 2} \\
& \text{ 21} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 7 \\
& 2 \\
\end{align} \right)=21$ and is the same as one obtained before.
(c)
The value of $\left( \begin{align}
& 12 \\
& 1 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& 12\text{ }nCr\text{ 1} \\
& \text{ 12} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 12 \\
& 1 \\
\end{align} \right)=12$ and is the same as one obtained before.
(d)
The value of $\left( \begin{align}
& 11 \\
& 1 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& \text{11 }nCr\text{ 1} \\
& \text{ 11} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 11 \\
& 1 \\
\end{align} \right)=11$ and is the same as one obtained before.
(e)
The value of $\left( \begin{align}
& 6 \\
& 6 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& \text{6 }nCr\text{ 6} \\
& \text{ 1} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 6 \\
& 6 \\
\end{align} \right)=1$ and is the same as one obtained before.
(f)
Obtain the value of $\left( \begin{align}
& 15 \\
& 2 \\
\end{align} \right)$ as follows:
$\begin{align}
& \text{15 }nCr\text{ 2} \\
& \text{ 105} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 15 \\
& 2 \\
\end{align} \right)=105$ and is the same as one obtained before.
(g)
The value of $\left( \begin{align}
& 100 \\
& 2 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& \text{100 }nCr\text{ 2} \\
& \text{ 4950} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 100 \\
& 2 \\
\end{align} \right)=4,950$ and is the same as one obtained before.
(h)
The value of $\left( \begin{align}
& 100 \\
& 98 \\
\end{align} \right)$ is found as follows:
$\begin{align}
& \text{100 }nCr\text{ 98} \\
& \text{ 4950} \\
\end{align}$
Thus, the value of $\left( \begin{align}
& 100 \\
& 98 \\
\end{align} \right)=4,950$ and is the same as one obtained before.