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Se poate să se calculeze [tex] C^{0}_{3}[/tex]? Mie îmi dă [tex] \frac{6}{0} [/tex]

Răspuns :

[tex]C^{0}_3=\frac{3!}{0!*(3-0)!}=\frac{6}{1*6}=1\\0!=1\\Demonstratie:\\ n!=1*2*3*...*n=\frac{(n+1)!}{n+1}\\3!=1*2*3=6\\2!=\frac{3!}{2+1}=\frac{6}{3}=2\\ 1!=\frac{2!}{1+1}=\frac{2}{2}=1\\0!=\frac{1!}{0+1}=\frac{1}{1}=1[/tex]