Question

Preciso de ajuda, por favor! ​

Answer 1

1)

a) $\frac{10!}{8!} = \frac{10.9.8!}{8!} =10.9 = 90$

b) $\frac{8!}{5!3!} = \frac{8.7.6.5!}{5!.3!} =\frac{8.7.6}{3!} =\frac{8.7.6}{3.2} = 8.7 = 56$

2)

a)$\frac{(n-4)!}{(n-3)!} = \frac{(n-4)!}{(n-3)(n-4)!} = \frac{1}{n-3}$

b)$\frac{(2n)!}{(2n-2)!} = \frac{2n.(2n-1)(2n-2)!}{(2n-2)!} = 2n(2n-1) = 4n^{2} -2n$

3)

$n^{2} .(n-2)!.(1-\frac{1}{n})=n^{2} .(n-2)!.(\frac{n-1}{n}) = n.(n-2)!.(n-1)\\n.(n-1)(n-2)! = n(n-1)!\\Resposta: D$