Mathematics, 23.03.2020 16:30 itzdulce

The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15candidates. Eightof 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?

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Answer from: xxtonixwilsonxx

a) 5.13% probability that all of the offices are filled by members of the debate team

b) 2.56% probability that none of the offices are filled by members of the debate team

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the people are chosen is important, since the first person is the president, the second is the vice president and so on... So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

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

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 8(candidates of the members debate team).

$D = P_{(8,4)} = \frac{8!}{(8-4)!} = 1680$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{1680}{32760} = 0.0513$

5.13% 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?

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 7(candidates who are not of the members debate team).

$D = P_{(7,4)} = \frac{7!}{(7-4)!} = 840$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{840}{32760} = 0.0256$

2.56% probability that none of the offices are filled by members of the debate team

Answer from: Quest

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

Answer from: Quest

on a coordinate grid, point a is at (−4.0, −2.4) and point b is at (4.0, −2.4). point b is a reflection of point a across the –axis. input either a lowercase x or i think is the right awnser

step-by-step explanation:

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