Factorials? Induction? (1 Viewer)

[PC]

Can anyone do anything with this?

Simplify:

n x (n – 1) x (n – 2) x ... x k x ... x 3 x 2 x 1
-----------------------------------------------------
(n – k + 1) x (n – k) x ... x 3 x 2 x 1

Thanks...

 

[study-freak]

n x (n – 1) x (n – 2) x ... x k x ... x 3 x 2 x 1
-----------------------------------------------------
(n – k + 1) x (n – k) x ... x 3 x 2 x 1

=n!/(n-k+1)!
=nP(k-1)
=n(n-1)(n-2)...(n-k+2)

 

[PC]

That's what I came up with too. I'm just wondering if there's supposed to be a simpler factorial notation that magically appears. It's stumped one of the 3u teachers at our school (and me).