Question

Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 27 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, Rebecca, and John are chosen

Answer 1

1/2925 = 0.0003 = 0.03% probability that you, Rebecca, and John are chosen.

Explanation:

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

In this question, the order in which the people are chosen is not important, so the combinations formula is used to solve the question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

Only 1 outcome in which these 3 people are selected, so
`D = 1`

Total outcomes:

3 people from a set of 27, so

`T = C_(27,3) = (27!)/(3!(27-3)!) = 2925`

Probability:

`p = (D)/(T) = (1)/(2925) = 0.0003`

1/2925 = 0.0003 = 0.03% probability that you, Rebecca, and John are chosen.