Question

Комбинаторика. Упростить!

Answer 1

$\frac{10!}{(10-2)!}+ \frac{10!}{(10-1)!}= \frac{10!}{8!}+ \frac{10!}{9!}= \frac{10!(9!+8!)}{9!8!}= \frac{10*8!(9+1)}{8!}=10*10=100$

второй пример

$(\frac{9!}{6!}- \frac{3!}{1!}): \frac{7!}{6!}= \frac{9!-3!6!}{6!}* \frac{6!}{7!}= \frac{6!(7*8*9-6)}{7!}= \frac{498}{7}=71 \frac{1}{7}$

Третий пример

$\frac{n!}{(n-5)!}:( \frac{n!}{(n-6)!}- \frac{n!}{(n-7)!})= \frac{n!}{(n-5)!}:( \frac{n!(1-n+6)}{(n-6)!})= \frac{n!(n-6)!}{(n-5)!n!(7-n)}}$

$\frac{(n-6)!}{(n-5)!(7-n)}= \frac{1}{(n-5)(7-n)}$

Answer 2

A=10!/(10-2)!+10!/(10-1)!=10!/8!+10!/9!=8!•9•10/8!+9!•10/9!=90+10=100