Answer
The number of ways in which a group of 3 members is to be selected out of 20 people to attend a conference is $1140$.
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=20 \\
& r=3 \\
\end{align}$
Then, we have to find the number of combinations of 20 things taken 3 at a time:
$\begin{align}
& {}_{20}{{C}_{3}}=\frac{20!}{3!\left( 20-3 \right)!} \\
& =\frac{20!}{3!17!} \\
& =\frac{20\times 19\times \ldots \times 17!}{3!17!} \\
& =1,140
\end{align}$
Thus, the number of ways in which a group of 3 members is to be selected out of 20 people to attend a conference is $1140$.
