Answer
The required number of ways to select the four-person committee from a group of 11 people is 330.
Work Step by Step
The order in which the four-person committee is selected does not matter. Thus, this is a problem of selecting 4 people from a group of 11 people. We need to find the number of combinations of 11 things taken 4 at a time.
Apply the formula,
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
Where $ n=11,r=4$
$\begin{align}
& {}_{11}{{C}_{4}}=\frac{11!}{\left( 11-4 \right)!4!} \\
& =\frac{11!}{7!\times 4!}
\end{align}$
Solving further,
$\begin{align}
& {}_{11}{{C}_{4}}=\frac{11\times 10\times 9\times 8\times 7!}{4\times 3\times 2\times 1\times 7!} \\
& =11\times 10\times 3 \\
& =330
\end{align}$
Hence, there are 330 ways to select the four-person committee from a group of 11 people.
