(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

C(n,3) = C(n,8)

2. Relevant equations

n!/(n-3)!3! = n!/(n-8)!8!

3. The attempt at a solution

My attempts at a solution are many and varied. But, I figure my problem is with the algebraic operations on factorials. Logically, since the numerators are both n!, I figure that I can ignore that and just work on (n-3)!3! = (n-8)!8!

I boiled this down to (n-3)!/(n-8)! = 6720. I solved this based on the fact that I know that 8!/3! = 6720. Therefore, (n-3)! = 8!, and n = 11. But this was simply guess work on my part. What I'm confused about is, what is the proper way to solve the problem? How do I perform algebra on these factorials?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Combination Problem

**Physics Forums | Science Articles, Homework Help, Discussion**