Lin and Kai are friends that work together on a team of n total people. Their manager is going to randomly select 2 people from the team of n to attend a conference. What is the probability that Lin and Kai are the 2 people chosen? Choose 1 answer:(Choice A) (2n)1(Choice B) (2n)(Choice C) n2(Choice D) n(n−1)2
Q. Lin and Kai are friends that work together on a team of n total people. Their manager is going to randomly select 2 people from the team of n to attend a conference. What is the probability that Lin and Kai are the 2 people chosen? Choose 1 answer:(Choice A) (2n)1(Choice B) (2n)(Choice C) n2(Choice D) n(n−1)2
Identify Team and Selection: Identify the total number of people on the team and the number of people to be chosen. Assume the team has 10 people and 2 are to be chosen.
Calculate Total Ways: Calculate the total number of ways to choose 2 people from 10. Use the combination formula: Number of ways=(210)=2×110×9=45
Determine Lin and Kai: Determine the number of ways to specifically choose Lin and Kai. Since they are only two people, there is only 1 way to choose both of them together.
Calculate Probability: Calculate the probability that Lin and Kai are the two chosen. The probability is the number of favorable outcomes divided by the total number of outcomes:P(Lin and Kai)=451