Question

resolva a seguinte expressão:
An,3=16.Cn,2

Answer 1

$\Bmatrix{A(n,p)= \frac{n!}{(n-p)!} \\\\C(n,p)= \frac{n!}{p!(n-p)!} \end$

e tbm 
$n! = n*(n-1)*(n-2)*(n-3)*(n-4)!....$


aplicando isso
$A(n,3) = 16*C(n,2)\\\\\frac{n!}{(n-3)!}= 16* \frac{n!}{2!(n-2)!} \\\\\frac{n!}{(n-3)!}= 8* \frac{n!}{(n-2)! }$

$\frac{1}{(n-3)!}= 8* \frac{1}{(n-2)!} \\\\\frac{1}{(n-3)!}= 8* \frac{1}{(n-2)*(n-3)!} \\\\1=8* \frac{1}{(n-2)} \\\\1*(n-2)= 8\\\\n=8+2\\\\n=10$