Question

There are 90 students in a classroom. How many relationships are there in this classroom? Show how you got this.
Hint: Consider this 2 students in the class would be 1 relationship, whereas 7 students in the class would yield 21 relationships.

What I think: I'm super stuck on this. I think you use factorials but how?

Answer 1

combinations of 2 at a time?
for example for 7 students
n!/[ 2! (7-2)! ]

= 7 /{2*5!}

= 7 * 6 /2 = 21 well that checks so

90! /[ 2!(88!) ]

= 90 * 89/2

= 45*89

= 4005

Answer 2

= 7! /{2*5!}

= 7 * 6 /2 = 21 well that checks so