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Lin and Kai are friends that work together on a team of nn total people. Their manager is going to randomly select 22 people from the team of nn to attend a conference. What is the probability that Lin and Kai are the 22 people chosen? Choose 11 answer:\newline(Choice A) 1(n2)\frac{1}{\binom{n}{2}}\newline(Choice B) (n2)\binom{n}{2}\newline(Choice C) 2n\frac{2}{n}\newline(Choice D) 2n(n1)\frac{2}{n(n-1)}

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Q. Lin and Kai are friends that work together on a team of nn total people. Their manager is going to randomly select 22 people from the team of nn to attend a conference. What is the probability that Lin and Kai are the 22 people chosen? Choose 11 answer:\newline(Choice A) 1(n2)\frac{1}{\binom{n}{2}}\newline(Choice B) (n2)\binom{n}{2}\newline(Choice C) 2n\frac{2}{n}\newline(Choice D) 2n(n1)\frac{2}{n(n-1)}
  1. 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 1010 people and 22 are to be chosen.
  2. Calculate Total Ways: Calculate the total number of ways to choose 22 people from 1010. Use the combination formula: \newlineNumber of ways=(102)=10×92×1=45 \text{Number of ways} = \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45
  3. Determine Lin and Kai: Determine the number of ways to specifically choose Lin and Kai. Since they are only two people, there is only 11 way to choose both of them together.
  4. 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:\newlineP(Lin and Kai)=145 P(\text{Lin and Kai}) = \frac{1}{45}

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