Asked by alex
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?
Answers
Answered by
Graham
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.
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.