Q1. A group of 20 children is seated in a circle. Each child is assigned a color green, yellow, or blue at random and independently.

What is the expected number of children who get the same color as the person on their left?

Q2. You generate a random permutation of 1, 2, 3, 4, 5. Let Xi denote the number at the ith position. What is the expected number of positions i at which i is a factor of Xi?