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?

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Answer 1 · 2018-02-25T11:05:26

Using permutation..

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

$!^{n} P_{r}$ $color(white)!^nP_r$

Where;

$n = no of supervisors$ $n = "no of supervisors"$

$r = taken supervisor$ $r = "taken supervisor"$

$n = 5$ $n = 5$

$r = 2$ $r = 2$

$!^{n} P_{r} = \frac{n!}{n - r}!$ $color(white)!^nP_r = (n!)/(n - r)!$

$\Rightarrow \frac{5!}{5 - 2}!$ $rArr (5!)/(5 - 2)!$

$\Rightarrow \frac{5!}{3!}$ $rArr (5!)/(3!)$

$\Rightarrow \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1}$ $rArr (5 xx 4 xx 3 xx 2 xx 1)/(3 xx 2 xx 1)$

$rArr (5 xx 4 xx cancel(3 xx 2 xx 1))/cancel(3 xx 2 xx 1)$

$rArr (5 xx 4)$

$rArr 20 ways$

Hence the sample of space would be In $20 ways$