1. binomials coefficients 2

Some one pls help me with this prob pls...*
Can someone simplify this?....thanks

$
N=(-1)^k(-n)(-n+1)...(-n+k-1)
=(-1)^k\binom{-n+k-1}{k}k!
$

can we use principle of mathematical induction with this? someone help me solve this problem pls

2. Work the other way around ... show that $(-1)^k\binom{-n+k-1}{k}k!
=(-1)^k(-n)(-n+1)...(-n+k-1)$

$\binom{a}{b}=\frac{a!}{b!(a-b)!}$

So $\binom{-n+k-1}{k}k!
=\frac{(-n+k-1)!k!}{k!(-n+k-1-k)!}=\frac{(-n+k-1)!}{(-n-1)!}$