Savanah Boone

2022-07-14

How do you determine the sample space for the experiment where two county supervisors are selected from five supervisors, A, B, C, D, E to study a recycling plan?

Jasper Parsons

Expert

Step 1
Since only two county supervisors are selected from the list of five supervisors, the formula would be;
${!}^{n}{P}_{r}$
Where
$n=\text{no of supervisors}$
$r=\text{taken supervisor}$
$r=\text{taken supervisor}$
$n=5$
$r=2$
Step 2
${!}^{n}{P}_{r}=\frac{n!}{n-r}!$
$⇒\frac{5!}{5-2}!$
$⇒\frac{5!}{3!}$
$⇒\frac{5×4×3×2×1}{3×2×1}$
$⇒\frac{5×4×\overline{)3×2×1}}{\overline{)3×2×1}}$
$⇒\left(5×4\right)$
$⇒20ways$
Hence the sample of space would be In 20ways.

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