Question

Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 19 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, Samuel, Lisa, and Andrew are chosen

Answer 1

Answer: the probability that I, Samuel Lisa and Andrew are chosen is 0.0003

Explanation:

Given that;

Number of 4 employees are to be chosen from 19 of them;

so Number of ways to choose 4 employees from 19 employees = ?

we know that;

c(n,r) =
`\left[\begin{array}{ccc}n\\r\end{array}\right]` = n! / ( r!(n-r)!)

so we substitute

c(19,4) =
`\left[\begin{array}{ccc}19\\4\end{array}\right]` = 19! / ( 4!( 19-4 )!) = 3876

so the probability that I, Samuel Lisa and Andrew are chosen will be;

⇒ 1 / 3876 = 0.0002579 ≈ 0.0003

the probability that I, Samuel Lisa and Andrew are chosen is 0.0003