Textbook problem: A teacher with a math class of 20 students randomly pairs the students to take a test. What is the probability that Camilla and Cameron, two students in the class, are paired with each other?
My answer: 1/190. There is only one such pair out of the 20-choose-2 possible pairings.
Their answer: 1/19. Camilla can be paired with 19 students and only one such pairing is with Cameron.
Question: What principle am I missing in my reasoning that would help me to see why their answer is right and mine wrong? It's like I follow their line of reasoning too but don't see what underlying assumption differentiates the answers to see how I can frame the problem correctly on my own.
Textbook: Chapter 26 from The Art of Problem Solving (Volume I) by Rusczyk and Lehoczky.
Best Answer
You're missing that the teacher will pair up all the students, making 10 pairs. Camilla and Cameron could be any of these 10.