# 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?

Feb 25, 2018

Using permutation..

#### Explanation:

Since only two county supervisors are selected from the list of five supervisors, the formula would be;

color(white)!^nP_r

Where;

$n = \text{no of supervisors}$

$r = \text{taken supervisor}$

$n = 5$

$r = 2$

color(white)!^nP_r = (n!)/(n - r)!

rArr (5!)/(5 - 2)!

rArr (5!)/(3!)

$\Rightarrow \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1}$

$\Rightarrow \frac{5 \times 4 \times \cancel{3 \times 2 \times 1}}{\cancel{3 \times 2 \times 1}}$

$\Rightarrow \left(5 \times 4\right)$

$\Rightarrow 20 w a y s$

Hence the sample of space would be In $20 w a y s$