Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 12 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Charles, Margaret, and Sean are chosen?

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joaobezerra joaobezerra · Answer 1 · 2022-07-20T21:48:27+02:00

Using the combination formula, it is found that the probability that you, Charles, Margaret, and Sean are chosen is:

[tex]p = \frac{1}{495}[/tex].

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 4 people will be chosen from a set of 12, hence the number of ways to choose them is:

[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]

The desired combination is only one, hence the probability is:

[tex]p = \frac{1}{495}[/tex].

More can be learned about the combination formula at https://brainly.com/question/25821700

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