The offices of president, vice president, secretary, and treasurer for an enviro

Question

The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 17 candidates. Eight of the candidates are members of the debate team.

(a) What is the probability that all of the offices are filled by members of the debate team?

(b) What is the probability that none of the offices are filled by members of the debate team? (

a) P(all offices filled by debate team members) =

(Round to three decimal places as needed.) (b)

P(no offices filled by debate team members=

(Round to three decimal places as needed.)

Explanation / Answer

ok , we know that the combination formula is given as

n C r = (n!)/(r!(n-r)!)

so number of ways in which 4 people can be selected from 17 people is

17 C 4 = (17!)/(4!(17-4)!)=2380

and number of ways in which 4 people can be selected from the debate team of 8

8 C 4 = (8!)/(4!(8-4)!)= 70 ,

so the probability for part a is

70/2380 = 0.029

b ) Probability that none of the office is filled by the debate team can be calculated simply as

17-8 = 9 the non debate team

or 9 c 4 = (9!)/(4!(9-4)!)= 126 ,

so the probability is 126/2380 = 0.052

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