Question

Calcule os números binomiais (10/6)​

Answer 1

Resposta:

210

Explicação passo-a-passo:

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$\mathtt{ \binom{10}{6} } \\ \\ \mathtt{ \frac{10!}{6! \times (10 - 6)!} } \\ \\ \mathtt{ \frac{10 \times 9 \times 8 \times 7 \times 6!}{6! \times (10 - 6)!} } \\ \\ \mathtt{ \frac{10 \times 9 \times 8 \times 7 \times 6!}{6! \times 4!} } \\ \\ \mathtt{ \frac{10 \times 9 \times 8 \times 7 \times \cancel{\blue {6!}}}{\cancel{\blue {6!}} \times 4!} } \\ \\ \mathtt{ \frac{10 \times 9 \times 8 \times 7}{4!} } \\ \\ \mathtt{ \frac{90 \times 8 \times 7}{4!} } \\ \\ \mathtt{ \frac{720 \times 7}{4!} } \\ \\ \mathtt{ \frac{5040}{4!} } \\ \\ \mathtt{ \frac{5040}{4 \times 3 \times 2 \times 1} } \\ \\ \mathtt{ \frac{5040}{12 \times 2 \times 1} } \\ \\ \mathtt{ \frac{5040}{24 \times 1} } \\ \\ \mathtt{ \frac{5040}{24} } \\ \\ \red{\mathtt{210}}$

Answer 2

Resposta:

210

Explicação passo-a-passo:

$\binom{10}{6} = \dfrac{10!}{(10 - 6)! 6!} \\ \binom{10}{6} = \dfrac{10!}{4! 6!} \\ \binom{10}{6} = \dfrac{10 \times 9 \times 8 \times 7 \times 6!}{4! 6!} \\ \binom{10}{6} = \dfrac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \\ \binom{10}{6} = \dfrac{5040}{24} \\ \boxed{ \boxed{ \underbrace{\binom{10}{6} =210}}}$