Question

Combinari de 2013 luate cate 2012-combinari de 2013 luate cate 1

Answer 1

$C^{2012}_{2013}-C^{1}_{2013}= \frac{2013!}{2012!*(2013-2012)!}- \frac{2013!}{1!*(2013-1)!}= \\ \\ = \frac{1*2*3*.....*2012*2013}{1*2*...*2012*1!}-\frac{1*2*3*...*2012*2013}{1*2012!}= \\ \\ =\frac{2013}{1}-\frac{2013}{1}= 0$

Answer 2

Cu formula

$C_n^k=C_n^{n-k}$, obținem:  $C_{2013}^{2012}=C_{2013}^1$, deci diferența lor este egala cu zero.