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.