Answer
The number of ways to select 18 people from 100 for the the required committee is $3.0664511e+19$.
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=100 \\
& r=18 \\
\end{align}$
Then, we have to find the number of combinations of 100 things taken 18 at a time:
$\begin{align}
& {}_{100}{{C}_{18}}=\frac{100!}{18!\left( 100-18 \right)!} \\
& =\frac{100!}{18!82!} \\
& =\frac{\left( \begin{align}
& 100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times \\
& 91\times 90\times 89\times 88\times 87\times 86\times 85\times 84\times 83\times 82! \\
\end{align} \right)}{\left( \left( 82! \right)\times 18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right)} \\
& =3.0664511e+19
\end{align}$
