Question

The offices of president, vice president, secretary, and treasures for an environmental club will be filled from a pool of 14 candidates Six of the candidates are members of the debate team. (a) What is the probability that all of the offices are filed by members of the debate team? (b) What is the probability that none of the offices are filled by members of the debate teams?

Answer 1

We will have the following:

a) The probability that all of the offices are filled by members of the debate team is:

`P=(6)/(14)\cdot(5)/(13)\cdot(4)/(12)\cdot(3)/(11)\Rightarrow P=(15)/(1001)`
`\Rightarrow P=0.01498501499\ldots\Rightarrow P\approx0.015`

b) We will have that the probability that none of the offices are filled with filled by memebers of the debate team is:

`P=(8)/(14)\cdot(7)/(13)\cdot(6)/(12)\cdot(5)/(11)\Rightarrow P=(10)/(143)`
`\Rightarrow P=0.06993006993\ldots\Rightarrow P\approx0.070`