Question

professor deu uns exercícios e eu não entendi praticamente nada, se alguém puder ajudar

1) Ap,3/Cp,4=12, qual o valor de p?
 2)Am,2/Cm,3 qual o valor de m?

Answer 1

$\frac{Ap,3}{Cp,4} = 4\\\\\\\ \frac{\frac{p!}{(p-3)!}}{\frac{p!}{4!(p-4)!}} = 4\\\\\\\ \frac{24(p-4)!p!}{p!(p-3)!}=4\\\\\ \frac{(p-4)!p!}{p!(p-3)!} = \frac{1}{6}$

$\frac{(p-4)!p!}{p!(p-3)!} = \frac{1}{6}\\\\\ \frac{(p-4)!}{(p-3)(p-4)!}=\frac{1}{6}\\\\ \frac{1}{(p-3)} = \frac{1}{6}\\\\\ (p-3) = 6\\\\ \boxed{p=9}$


$\frac{Am,2}{Cm,3} = 1\\\\\ \frac{\frac{m!}{(m-2)!}}{\frac{m!}{3!(m-3)!}} =1\\\\\\ \frac{9(m-3)!m!}{m!(m-2)!} = 1\\\\\ \frac{(m-3)!}{(m-2)(m-3)!}=\frac{1}{9} \\\\\\ m-2 = 9\\\\\ \boxed{m=11}$