Question

Three volunteers are chosen at random from a group of 20 people to help at a camp. How many unique groups of volunteers are possible?

Answer 1

In mathematics, a combination is a selection of items from a set that has distinct members

Formula

`^n_{^{}}C_r=\frac{n\text{ !}}{(n-r)!r!}`

Where

n = 20

r =3

`\begin{gathered} ^(20)C_3=\frac{20\text{ !}}{(20-3)!3!} \\ \\ \\ ^(20)C_3=\frac{20\text{ !}}{17!3!} \\ \\ \\ ^(20)C_3=\frac{20\text{ }*19*18*17!}{17!3!} \\ ^(20)C_3=\frac{20\text{ }*19*18}{3!} \\ \\ ^(20)C_3=\frac{20\text{ }*19*18}{3*2*1} \\ ^(20)C_3=\frac{20\text{ }*19*18}{6} \\ \\ ^(20)C_3=20\text{ }*19*3 \\ \\ \\ ^(20)C_3=1140 \end{gathered}`

The final answer

1140 unique groups of volunteers are possible