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Lin and Kai are friends that work together on a team of $n$ total people. Their manager is going to randomly select $m$ people from the team of $n$ to attend a conference. What is the probability that Lin and Kai are the $m$ people chosen?

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Find probabilities using the addition rule

Full solution

Q. Lin and Kai are friends that work together on a team of

n

total people. Their manager is going to randomly select

m

people from the team of

n

to attend a conference. What is the probability that Lin and Kai are the

m

people chosen?

Calculate Total Ways: Calculate the total number of ways to choose $2$ people from a team of $8$ . We use the combination formula: $nCr = \frac{n!}{r!(n-r)!}$ , where $n$ is the total number of items, and $r$ is the number of items to choose. Here, $n=8$ and $r=2$ .
Calculate Favorable Outcomes: Calculate the number of favorable outcomes, which is the specific scenario where Lin and Kai are chosen. Since they are only two people, there is only $1$ way to choose both of them together.
Calculate Probability: Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes.

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