Question

Calcule o valor de C5,3

Answer 1

        5!      =       5!   ==>  5.4.3!  ==> 5.4==> 10
      3!(5-3)!       3!2!           3!.2.1          2

Answer 2

$\boxed{\boxed{Ola\´ \: \: Fabiana} }$

$C_{5,3}$

• A combinação simples é definida por:

$C_{n,p} = \frac{n!}{p!(n-p)!}$

Onde:
$\begin{cases} n = 5 \\ p = 3 \\ C_{5,3} = ? \end{cases}$

Logo, teremos:

$\Leftrightarrow C_{5,3} = \frac{5!}{3!(5-3)!} \\ \\ \Leftrightarrow C_{5,3} = \frac{5 \cdot 4 \cdot \cancel{3!} }{ \cancel{3!} \cdot 2!} \\ \\ \Leftrightarrow C_{5,3} = \frac{20}{2 \cdot 1} \\ \\ \Leftrightarrow C_{5,3} =\frac{20}{2}$

$\Leftrightarrow \boxed{\boxed{C_{5,3} = 10} }} \end{array}\qquad\checkmark$

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