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

The sample space is:

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

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}=(5!)/(2!(5-2)!) =(5!)/(2!* 3!) = 10`

The sample space will consist of 10 combinations.

The sample space is:

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