Question

Liz is a student in Ms. Xu's class. Liz says to her classmates, "Of all the pairs of students Ms. Xu can choose as class leaders, I am included in one-tenth of those pairs." How many students are in Ms. Xu's class?

Answer 1

Assuming that all of the students in the class could be selected without bias.

The count of ways to select any 2 students from a class of size n, is:
{n!}/{2!*(n-2)!}

The count of ways to select Liz and any one other student from the class is:
(n-1)

If Liz's statement is accurate then:
1/10 = {(n-1)*2!*(n-2)!}/{n!}

Simplify and solve for n, the count of students in the class.