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combinari de 2011 luate cate 2 - combinari de 2011 luate cate 2009

Răspuns :

[tex] \binom{2011}{2} = \frac{2011!}{2! - (2011-2)!} = \frac{2011!}{2009! - 2!} [/tex]

[tex] \binom{2011}{2009} = \frac{2011!}{2009! - (2011-2009)!} = \frac{2011!}{2009! - 2!} [/tex]

\binom{2011}{2} - \binom{2011}{2009} = 0