Hey, thanks for reading this. I'm having trouble with a particular problem, and it goes:
The number of arrangements of 2n+2 different objects taken n at a time is to the number of arrangements of 2n different objects taken n at a time as 14:5. Find the value of n.
For this I gather that:
arrangements of 2n+2 objects : arrangements of 2n objects = 14:5
However, I don't understand the taken n at a time part...does that mean 2n+2 objects arranged in n spaces?
If so, would that be the same as saying:
(2n+2)! / (2n+2-n)! : (2n)! / (2n-n)! = 14:5
I've also thought about simplify it to (2n+2)(2n+1)(2n)! / (2n+2-r)(2n+1-r)(2n-r)! so to make it similar to the RHS.
Ayy input or insight would be sincerely appriciated.
Thanks!
-EDIT- Don't worry, after a bit of re-reading, I figured it out.