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;

#color(white)!^nP_r#

Where;

#n = "no of supervisors"#

#r = "taken supervisor"#

#n = 5#

#r = 2#

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

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

#rArr (5!)/(3!)#

#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#