Question

calcule o número binominal 6/2+5/3-12/12​

Answer 1

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Binomial de um número

$\huge\boxed{\boxed{\boxed{\boxed{\sf\binom{n}{k}=\dfrac{n!}{k!\cdot(n-k)!}}}}}$

$\displaystyle\sf\binom{6}{2}=\dfrac{6!}{2!\cdot(6-2)!}\\\sf \binom{6}{2}=\dfrac{6!}{2!\cdot4!}=\dfrac{\diagup\!\!\!6\cdot5\cdot\diagdown\!\!\!\!\!4!}{\diagup\!\!\!2\cdot1\cdot\diagdown\!\!\!\!\!4!}=3\cdot5=15\\\sf\binom{5}{3}=\dfrac{5!}{3!\cdot(5-3)!}=\dfrac{5\cdot4\cdot\diagup\!\!\!\!3!}{\diagup\!\!\!3!\cdot2!}=10\\\sf\binom{12}{12}=1$

$\displaystyle\sf\binom{6}{2}+\binom{5}{3}-\binom{12}{12}=15+10-1\\\huge\boxed{\boxed{\boxed{\boxed{\displaystyle\sf\binom{6}{2}+\binom{5}{3}-\binom{12}{12}=24}}}}\checkmark$

Answer 2

Resposta:

24

Explicação passo-a-passo:

$\blue {{ _{\heartsuit} } \heartsuit_{\heartsuit} } \: \: \mathsf {OI, TUDO \: \: J\acute{O}IA \: ? \: \:\blue {{ _{\heartsuit} } \heartsuit_{\heartsuit} } }$

$\mathtt{ \binom{6}{2} + \binom{5}{3} - \binom{12}{12} } \\ \\ \mathtt{ \frac{6!}{2! \times (6 - 2)!} + \frac{5!}{3! \times (5 - 3)!} - \binom{12}{12} } \\ \\ \mathtt{ \frac{6!}{2! \times (6 - 2)!} + \frac{5!}{3! \times (5 - 3)!} - 1 } \\ \\ \mathtt{ \frac{6 \times 5 \times 4!}{2! \times 4!} + \frac{5!}{3! \times (5 - 3)!} - 1} \\ \\ \mathtt{ \frac{6 \times 5 \times 4!}{2! \times 4!} + \frac{5 \times 4 \times 3!}{3! \times 2!} - 1} \\ \\ \mathtt{ \frac{6 \times 5 \times \cancel{\blue {4!}} }{2! \times \cancel{\blue {4!}}} + \frac{5 \times 4 \times\cancel{\blue {3!}} }{\cancel{\blue {3!}} \times 2!} - 1} \\ \\ \mathtt{ \frac{6 \times 5}{2!} + \frac{5 \times 4}{2!} - 1 } \\ \\ \mathtt{ \frac{30}{2} + \frac{20}{2} - 1} \\ \\ \mathtt{15 + 10 - 1} \\ \\ \mathtt{25 - 1} \\ \\ \huge\red{\mathtt{24}}$

$\mathcal{ATT : ARMANDO}$