+0  
 
0
80
4
avatar

Simplify $\dfrac{\dbinom{n}{k-1}}{\dbinom{n}{k-2}}$. Thank you!

 Jun 13, 2021
edited by Guest  Jun 13, 2021
 #1
avatar
0

This simplifies to n/(n - k).

 Jun 13, 2021
 #2
avatar
0

please explain. thanks

Guest Jun 13, 2021
 #3
avatar+287 
+1

The closed-form formula for $\binom{n}{k}$ is $\frac{n!}{k!(n-k)!}$.   So we can express both numberator and denominator by its closed-form formula and then do some algebra.   The final result comes out very simple: three simple terms numerator, and 2 simple terms denominator.
 

 Jun 13, 2021
 #4
avatar
0

okay thanks.

Guest Jun 15, 2021

20 Online Users

avatar
avatar
avatar
avatar