Răspuns:
[tex]A^{123}_{2012} = \dfrac{2012!}{(2012-123)!} = \dfrac{2012!}{1889!}[/tex]
[tex]C_{2012}^{123} \cdot P_{123} = \dfrac{2012!}{123!(2012-123)!} \cdot 123! = \dfrac{2012!}{1889!}[/tex]
[tex]\Rightarrow A^{123}_{2012} = C_{2012}^{123} \cdot P_{123}[/tex]
q.e.d.
✍ Reținem formulele
[tex]\boldsymbol{A_{n}^{k} = \dfrac{n!}{(n - k)!}}[/tex]
[tex]\boldsymbol{C_{n}^{k} = \dfrac{n!}{k!(n - k)!}}[/tex]
[tex]\boldsymbol{P_{n} = n!}[/tex]
