I'm wondering why my answer here is incorrect.
The question is: John and Steve are members of a class of $20$ students. What is the probability that they are paired together?
My thought was simply $1$ way to pair John and Steve and $20 \choose 2$ total pairs so $\frac{1}{190}$. But the correct answer is $\frac{1}{19}$. How is it that my method doesn't work?
Best Answer
You calculated the number of combinations of two people selected from a class of 20.
Consider how many people John could be paired with: There are 19 other students in the class. There is one chance in 19 that John's partner will be Steve.