Question

Resolva as Análise Combinatória:a)C 5,4
b)7!5!/4!3!

Answer 1

a) $\boxed{C_{m,n} = \frac{m!}{n! \cdot (m-n)!}}$

$C_{5,4} = \frac{5!}{4! \cdot (5-4)!} \\\\ C_{5,4} = \frac{5!}{4! \cdot 1!} \\\\ C_{5,4} = \frac{5 \cdot 4!}{4!} \\\\ \boxed{\boxed{C_{5,4} = 5}}$


b) $\frac{7! \cdot 5!}{4! \cdot 3!} \\\\ \frac{7 \cdot 6 \cdot 5 \cdot 4! \cdot 5!}{4! \cdot 3!} \\\\ \frac{7 \cdot 6 \cdot 5 \cdot 5 \cdot 4 \cdot 3!}{3!} \\\\ 7 \cdot 6 \cdot 5 \cdot 5 \cdot 4 = \boxed{\boxed{4200}}$

Answer 2

:a)C 5,4  =    5!     =  5. 4!  = 5
                4!(5-4)!      4!1!

b)  7! 5! = 7.6.5.4!.5.4.3!  = 7.6.5.5.4 =  4200
     4!3!            4!.3!