Chapter 11.2, Problem 27S

To determine

To find: The number of possibilities.

Answer to Problem 27S

The number of possibilities are $28$ .

Explanation of Solution

The permutations are for lists(order matters) and combination are for groups(order doesn’t matter).

Since the order is not important in selecting the employees, then the situation is a combination.

The combination formula is given as:

  $C\left(n,r\right)=\frac{n!}{\left(n-r\right)!r!}$

There are eight employees taken two at a time, so the number of possibilities are given as:

  $\begin{array}{c}C\left(8,2\right)=\frac{8!}{\left(8-2\right)!2!}\\ =\frac{8!}{6!2!}\\ =28\end{array}$

Therefore the number of possibilities are $28$ .