Question

Find the sample space for the experiment.
Two county supervisors are selected from five supervisors, A, B, C, D and E, to study a recycling plan.

Answer 1

Answer:

The sample space is:

$AB,\ AC,\ AD,\ AE,\\BC,\ BD,\ BE\\CD,\ CE\\DE$

Step-by-step explanation:

The sample space of an experiment is a set of all the possible values that satisfies that experiment.

The five supervisors are A, B, C, D and E.

Two are to selected.

The number of ways to select 2 supervisors  from 5 is: ${5\choose 2}=\frac{5!}{2!(5-2)!} =\frac{5!}{2!\times 3!} = 10$

The sample space will consist of 10 combinations.

The sample space is:

$AB,\ AC,\ AD,\ AE,\\BC,\ BD,\ BE\\CD,\ CE\\DE$