Precalculus (6th Edition) Blitzer

The number of ways in which a group of 3 members is to be selected out of 20 people to attend a conference is $1140$.
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 $1140$.