Ai aranjamente și combinări
[tex]\boldsymbol{A_{n}^{k} = \dfrac{n!}{(n - k)!}}[/tex]
[tex]A_{10}^{2} = \dfrac{10!}{(10 - 2)!} = \dfrac{10!}{8!} = \dfrac{8! \cdot 9 \cdot 10}{8!} = 90[/tex]
[tex]\boldsymbol{C_{n}^{k} = \dfrac{n!}{k!(n - k)!}}[/tex]
[tex]C_{10}^{2} = \dfrac{10!}{2!(10 - 2)!} = \dfrac{10!}{2! \cdot 8!} = \dfrac{8! \cdot 9 \cdot 10}{1 \cdot 2 \cdot 8!} = 45[/tex]
[tex]C_{10}^{8} = \dfrac{10!}{8!(10 - 8)!} = \dfrac{10!}{8! \cdot 2!} = \dfrac{8! \cdot 9 \cdot 10}{8! \cdot 1 \cdot 2} = 45[/tex]
Rezultatul calcului:
[tex]\dfrac{C_{10}^{2} + C_{10}^{8}}{A_{10}^{2}} = \dfrac{45 + 45}{90} = \dfrac{90}{90} = \bf 1[/tex]
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